A Syrian mother, trying to make a new home but pulled by pleas from those she left behind.

Thousands of Canadians enlisted in an unusual mission to help Syrian refugees start new lives. Now they face a gut-wrenching issue: the relatives half a world away.

TORONTO – Sept. 8, morning

Wissam al-Hajj, a Syrian refugee, woke up in the most comfortable home she had ever lived in, an apartment growing increasingly stuffed with toys for her four children. She realized she had slept far more soundly than usual. But when she remembered why, she grew irritated: Her husband, Mouhamad, had hidden the phone from her.

As their older children competed for the first shower, Ms. Hajj recalled the argument from the night before. Her husband had been trying to spare her from an agonizing consequence of their move to Canada: the pleading messages from family members and friends across the Middle East.

“I’m only going to give it to you if you stop talking to them at night,” he had said to her.

“I’m going to start working and buy my own phone,” she had shot back, the threat hollow but deeply felt.

Seven months earlier, the couple had been catapulted to a new life. As many other nations were shunning refugees, a group of Canadian strangers had essentially adopted the family for a year, an effort repeated thousands of times across the country. In Lebanon, where the family had fled from Syria, the children used to work for a dollar a day and cry as they watched others board school buses. Now, attending school for the first time in their lives, they treated the morning like a race: poised to go, ready with new backpacks and insulated lunchboxes an hour before the bus arrived.

The family was living through the first refugee crisis in history in which people without countries or homes could communicate instantaneously with one another. Previous generations of refugees often ached for any information about relatives, but now messages zipped back and forth around the world on free apps. The joy of such regular communication came at a steep cost: constant updates on the misery of relatives left behind, intensifying worry and impeding progress for those trying to carve out a new life. The Hajjes’ phone pulsed with voice messages in Arabic:

Enjoy every sip of cold water, because I have none. Your brother was jailed because his papers expired. He needs $900 to renew them or he will be arrested again. Can you bring us to Canada?

The couple heard that last question as many as 20 times a day. If the messages arrived while Mr. Hajj was grocery shopping, he would blank on which items to buy, instead becoming lost in questions. The couple had just arrived in Canada with one piece of luggage and almost no money of their own, so what could they do? Which relative would they even try to help first — his brother or her brother, or one of the dozens of others?

Sometimes Mr. Hajj did not respond to the messages because he had no idea what to say. When he and his wife did reply, they left out some details of just how different their lives had become.

In Lebanon, which has been flooded with refugees, passers-by cursed the family’s relatives for being Syrian. In Canada, just the evening before, an older couple had approached the Hajjes in the park, asked, “Syrian?” and insisted on sharing their phone numbers in case they could do anything for the newcomers. As one of Ms. Hajj’s brothers was scrambling to find the money to stay out of jail, the Salvation Army gave the Hajjes a gift card for about the same amount, letting them refurnish their three-bedroom apartment overlooking lush foliage in Toronto.

(In an earlier article on the private sponsorship of refugees in Canada, the couple used part of their family name, Ahmed, because of safety concerns. They have since given permission to use their official surname, al-Hajj.)

After the children left for school, Mr. Hajj picked up his own new backpack and headed to English class. He was focused on moving forward, on seizing every opportunity he could. In Syria, he had been a farmer and shepherd. Now, at 36, he was finally learning to read and write, and in an entirely new language.

That morning, he was the star of his class. His nice-to-meet-yous made his teacher’s dangling earrings sway as she nodded approval, and he helped a Mandarin speaker who was struggling to fill out a work sheet. To his amazement, the English words he heard outside class were beginning to mean something. In the opaque lottery of the refugee system — this family goes here, that family stays there — many people ended up with diminished lives, but he and his children had better prospects than ever before. “What’s happening now is something we never dreamed in Syria or Lebanon,” he said.

Sometimes he was fatalistic about the messages from home; in black-humor moments, he commented that he and his wife should stop listening to them.

Ms. Hajj, however, often stayed up for much of the night to converse with relatives seven hours ahead, growing weepy and exhausted by dawn. Like many of the relatives, she had never learned to read or write, so they used WhatsApp to volley short voice recordings. Those messages felt like a lifeline, and the ones that were not harrowing were comforting: greetings for the Eid al-Adha holiday among her 16 half and full siblings, and a running whose-baby-is-cuter photo contest. Sometimes she woke her 10-year-old son, Majed, in the middle of the night for technical help.

She was trying to embrace life in Canada, cheering during her children’s soccer matches and soaking up advice on tummy time and solid food for her 5-month-old, Julia. But her husband worried that the infusions of survivor’s guilt were preventing her from fully entering her new world. She often seemed more connected to the electronic constellation of relatives back home than to the Toronto streets she did not know and the English signs she could not decipher. When the sponsors tutored her in English, she often yawned through the lessons.

Now, alone with Julia, Ms. Hajj played another request that had just arrived, this one from a sister-in-law in Lebanon.

We just want to thank you in advance for anything you can do. We would be forever grateful to you if this happened.

The two women were close. Eman Khalaf, the voice on the phone, was married to Mouhamad’s younger brother Ali. The two couples had lived side by side in their village south of Aleppo, then in adjacent tents in a refugee camp in Lebanon. The day before, Mouhamad had told Ali that school was starting in Canada, and he had replied:

I envy you so much, your kids will visit us when they are doctors and engineers.

The brothers had dreamed of reuniting in Canada. Mouhamad had promised his younger brother that he would take up the cause with the sponsors who were resettling his family.

The grandmotherly group had become the Hajjes’ funders, chauffeurs, tutors and all-around tacticians. Julia had never been held by her real extended family; her parents’ new living room displayed photographs of her and her siblings with the sponsors’ grandchildren. The sponsors had found schools, doctors, clothes, summer programs and bikes for the children. When those first bikes were stolen, they got new ones. The weather was still sweltering, but they had already outfitted the older children with head-to-toe ice-skating gear. A few nights before, a fire alarm had woken the Hajjes, but because the sponsors had thought to explain what to do, they exited the apartment calmly.

Because of the care the sponsors took, Ms. Hajj said she had no worries about her immediate family’s future in Canada. She felt especially close to Peggy Karas, a former geography teacher whose slight air of sternness belied her generosity. Sometimes when she saw Ms. Karas at her door, the older Canadian woman straining a bit under the heavy bags of fruit and halal meat she had brought, Ms. Hajj’s eyes welled in gratitude. “I feel like Peggy is like my friend, my mom, my sister,” she said.

The Hajjes’ best hope for helping their relatives, they believed, lay with Ms. Karas and her partners, who could sponsor additional family members or find other Canadians to do so. Ms. Hajj had already blurted out requests for the sponsors to bring over her brother Ibrahim.

But her husband had not yet said a word to the sponsors about his own brother. He intended to, but his concern for his distraught wife stopped him: Perhaps she needed a relative more. “Maybe if someone from her family comes here, she will feel better,” he said.

Asking the sponsors about more than one relative seemed like too much. The Hajjes cringed at making requests of their patrons or doing anything that could seem like taking advantage. Even when Mr. Hajj’s father asked the couple for money, a humiliating request for the older man, they did not feel they could siphon from the allowances the sponsors had given them.

“They’re giving us all of this, with nothing in return, and we have to bother them with other requests as well?” Ms. Hajj asked.

She had little idea that her inquiries, conveyed in gestures and broken English, were pushing the volunteers into conversations they had never anticipated. Something similar was happening all over Canada. Thousands formed groups to sponsor one family for one year, to give their time and money to initiate the new arrivals into Canadian life. But thanks in large part to cellphones and social media, Canadians with no prior connection to the Middle East were getting glimpses into the well of desperation that was the refugee crisis.

They found themselves confronting quandaries: When an infant relative in Jordan needed surgery her parents could not afford, should the sponsors reach into their pockets to pay? Was it better to invest everything in resettling one family or to spread the resources between two? Should the Canadians select which relatives to help, to spare the Syrian newcomers from choosing?

Even though they had already responded to the refugee crisis more generously than many people across the world, was it enough? Where did it stop?

BAR ELIAS, Lebanon – Sept. 9, morning

As Mouhamad al-Hajj was sleeping in his handsome new bed in Toronto, his brother Ali stood at a dusty crossroads halfway around the world, a few miles from the Syrian border. He was one of the million-plus refugees in Lebanon, another face in a cluster of laborers waiting all day at the intersection for a chance to work. Even if one of the trucks rumbling by stopped, work was not a sure thing. Sometimes the men would rush the vehicle, piling onto the back, and the strongest would force the others off, winning the job. Ali al-Hajj, 30, made it once every five or 10 days at best.

The youngest worker in the crowd was 13. Ali dreaded that his own children could be in that position one day. “I don’t care about money; all I care about is giving a proper education to my kids,” he said. He was counting on his brother in Canada for that chance.

The two used to stand at the intersection together, looking like a matched set with their skinny frames. They had lived in tandem since childhood. Mouhamad was the one who had spotted Eman as a potential wife for his younger brother. When the Hajjes lost their fourth child, shortly after birth, in Lebanon last year, the two brothers stood shoulder to shoulder to dig the tiny grave.

They were at work last winter, tiling a roof, when Mouhamad’s phone rang and a voice from the United Nations said his family had been chosen to move to Canada. He accepted immediately, but when he hung up he was reeling. He asked Ali if he should really leave his relatives for a country where he knew no one.

“Go,” his brother told him. “Just go. Don’t think about it.” Ali threatened to forge Mouhamad’s papers and travel in his place if he did not proceed.

That was when Mouhamad promised to try to bring the younger man to Canada. “If I have anyone in mind, it will be you,” he said.

There was no work for Ali that Friday, so he returned for lunch to the 6-by-10-foot shed, not really a home, where he, Eman and their three children lived. The shelter was so cramped that they often slept outside during the summer. Ali did not want his older children, 5 and 3, to feel deprived, so he sometimes brought home candy even though he could not afford it. He owed the grocery store down the road over $400.

That was far from his greatest worry. He feared that his family had no prospects: no ability to return to Syria, no ticket out of Lebanon, no education. His 5-year-old daughter, Nihal, longed to attend school, but he could not afford to send her. She sat in the shed and tried to write, holding pencil over paper. There was no one to teach her — her parents were illiterate, too.

In Lebanon, “there is no future,” Ali said as his children clambered onto his lap. “There is nothing.”

In his mind, his only way out would be for his brother to bring him to Canada. Like Mouhamad, he had registered as a refugee with the United Nations, a first step to putting him on a giant waiting list that could lead to a new life in a new country. Many nations were hesitant to accept new refugees, while others were already overwhelmed. The United States had accepted 10,000 Syrians in the previous year, far fewer than Canada. While it was considering testing a small Canadian-style sponsorship program, there were no firm plans yet.

Even in Canada, the fervor to sponsor refugees had calmed since last winter. Still, a request by sponsors might be Ali’s best shot. With many Syrians eager to relocate to Canada, his application might not be reviewed until 2017 or 2018, but at least he would be in line, with backers who would help resettle him and pay many of the costs.

He even spoke about it with Ibrahim, Wissam al-Hajj’s brother, who lived close by, and they figured that Ali’s family should go to Canada first because Ibrahim, who lives with his in-laws, could not leave them behind.

As Ali’s family finished a modest lunch, he returned to the intersection in case work came along. He would wait patiently for good news from Canada, staying closely connected to his brother through the phone. “We are really involved in each other’s lives,” he said. “We tell each other everything.”

But for all of the brothers’ instant communication, some things were too difficult to say. Ali had no idea that Mouhamad had not yet fulfilled his promise to make his case, or that the Canadian sponsors barely knew he existed.

TORONTO – Sept. 8, afternoon

After a morning at an art exhibit, Peggy Karas arrived at the Hajj apartment just as Mouhamad and the children were returning from school. She entered with a long to-do list: Remind Ms. Hajj of her first-ever teeth-cleaning appointment. Check in about sign-ups for swimming classes. Slip a few dollars to 8-year-old Moutayam to pay for his school assignment book. She told his parents to check it regularly, even though she knew they were unlikely to understand a word.

In the past seven months, Ms. Karas’s leisurely retirement — theater tickets one day, a quilting group the next — had veered in a direction she had never anticipated. As strange as it sounded, she had become a maternal figure to a woman to whom she could barely speak.

Initially, she thought sponsorship would be a matter of “O.K., yes, we’ll give you money,” as she put it. But the relationship had taken on a depth she had never predicted. Ms. Hajj had arrived in Canada in her final trimester of pregnancy, and when the older woman learned that the Syrian mother had lost her last baby, she devoted herself to seeing this one into the world. At 68, she wanted grandchildren, but none had yet arrived. Here were four children who needed help, the oldest three delighted by things Canadians took for granted — new pencils, popcorn at the movies, a soccer goal with a net. Like a real grandmother, she often found herself thinking about them during the day, wondering what they were up to.

“I never expected to be doing as much as I’m doing, and I’m loving what I’m doing,” she said.

But behind each of her agenda items that day was one overwhelming worry. The Hajjes were supposed to be self-sufficient by next February, but she feared they had virtually no chance of succeeding. They could not fill out a permission slip, read a medicine label, pay a bill or navigate the subway to a new destination on their own.

Together, the sponsors had more than a century of experience teaching school, yet they struggled to propel the family to basic literacy. Mr. Hajj’s triumphs in English class, like counting the capital letters in a sentence, shrank next to the magnitude of what he had to learn. When the sponsorship year ended in less than six months, he would need a job, but that could mean he would have less time — or none — for language instruction. The Canadian government had already funded part of the Hajjes’ integration, and without financial support from the sponsors, they might have to go on welfare.

“What kind of work is Mouhamad ever going to get?” Ms. Karas asked later. With his limited skills, working in a fast food kitchen or doing manual labor might be the best-case scenario. “No matter how hard he tries, he may never really speak English well, and that will really limit him,” she said.

The sponsors tutored his wife three times a week, going over the same words a 1-year-old learns: dog, ball, banana. Recently, Ms. Hajj had thrown out the soccer schedule the sponsors had left — the words were meaningless. Now Ms. Karas pointed to the new school bus schedule the Canadians had typed up. “Wissam, no garbage!” she said.

As Carole Atkins, another sponsor, distributed homemade cookies, Moutayam leapt from the couch to the floor and showed off his English in short but emphatic bursts. Asked whether he had music in his fourth-grade class, he answered by calling out the name of the national anthem: “O Canada!” Did he have Syrian children in his class? “So! Many!” When he overheard the sponsors’ saying that community pools were closing for the season, he interrupted with a suggestion: “Beach!”

But written language was something else. “We think the kids are doing great, and then you realize they can’t read a single word,” Marg Ewing, another sponsor, said earlier. Over the summer, another member of the group had brought the children workbooks. Majed, entering sixth grade, tried to do the first-grade exercises, then tore up the book in frustration.

The doting sponsors kept vowing to do less for the family, hoping to foster progress. But on every visit, they seemed to take on more. With the school year starting, they were contemplating adding a daily hour of afternoon homework assistance. Having invested many months, tens of thousands of dollars and their own hearts in the Hajjes’ success, they found themselves in a paradoxical situation: Getting the family to become truly independent required more and more help.

A month before, the volunteers had gathered at Ms. Karas’s house to discuss whether they could sponsor the Hajj relatives. They were now seeing the faraway crisis up close, through photos that flicked across the couple’s phone. Some other sponsor groups in Toronto had connected more directly with those marooned in the Middle East, exchanging messages with them on Facebook and using Google Maps to understand their journeys to find shelter from bombardment. More than a few groups were starting the paperwork and fund-raising to bring over relatives.

As the sponsors sat around Ms. Karas’s kitchen table, they had no idea that a man whose name they did not know was waiting for their answer. The women had no way of seeing the daily flood of pleas to the Hajjes, the depths of Wissam’s misery or Mouhamad’s struggle to work up the courage to ask them about his brother. The sponsors had not even planned the discussion. Ms. Ewing raised the topic only because Wissam kept mentioning her brother Ibrahim — who had not even filed the necessary paperwork, as far as the sponsors could tell.

Ms. Ewing was in favor of plunging in. But she thought of her own adult daughter, disabled and living in a group home, whom she tried to visit as much as possible. She decided not to make a case for doing more.

After just a few minutes, the sponsors arrived at a unanimous conclusion: They could not help the Hajjes bring over their family members, not with them so far from settled. The Canadian women saw sponsorship like a life raft: If you overloaded it, you risked sinking those you were trying to rescue.

“We want to do a really good job and get this family on their feet,” Ms. Karas said. “We can’t take on any more right now.”

No one from the sponsor group shared the decision with the Hajj family. For all of their newfound closeness, some things were too difficult to say.

Maybe some of the sponsors would move ahead in a year or two, Ms. Karas said later. Perhaps another group of volunteers would take on some family members, she said. Or the Hajjes would eventually bring relatives over themselves.

Back in the family’s apartment, Ms. Karas said goodbye, but minutes later she was back upstairs. A friend had just called to ask if he could hire Mr. Hajj for some gardening work over the weekend. He was interested, but the destination was near an unfamiliar subway station across town. So Ms. Karas volunteered for another task.

“Saturday, 8 o’clock, Peggy, Mouhamad, subway,” she confirmed on the way out.

The older children headed downstairs in the late summer dusk to practice at a makeshift soccer goal behind the apartment building. Ms. Hajj was tired, so when Zahiya, 10, returned inside and cleaned the kitchen, her mother settled down to sleep.

But at 1:30 a.m., Ms. Hajj awoke. It was already morning in the Middle East. She reached through the dark for the phone.