The group finally headed off in good spirits. Mr. Ramos had sold his motorcycle to pay the smuggler, telling his mother he would not need it anymore. She packed him a waterproof bag with some meager belongings: soap, toothpaste, antibiotics and a few clothes. A van arrived and they left.

That afternoon, they arrived at the rendezvous point with the smuggler, a town called Tucacas. They stayed the night in a hostel there. The motor of one of the boats had failed recently, something that worried Mr. Ramos when he wrote to a friend who had agreed to meet him in the jungle once he landed in Curaçao.

“It’s O.K. man… just relax, you’ll be here soon,” the friend wrote in Facebook message that Mr. Cordero forwarded to his mother.

“Yes bro, tomorrow, God willing,” Mr. Ramos wrote back.

Mr. Cordero climbed aboard the boat and sent a selfie to his sister. He wore yellow board shorts and no shirt, making a peace sign with his hands.

It was the last anyone heard from anyone in the group.

The first to know something had gone wrong was Ms. Ramos. The friend in Curaçao wrote over Facebook that he had waited all night but her son never arrived.

“I cried all night,” she said.

Questions haunt the families of the lost migrants each time they look out toward the sea. Could the men still be alive somehow? Will Venezuela ever return to the country that it was, one where it was not necessary to swim to the shore in Curaçao after being tossed from a fishing boat?

Ms. Ramos is still waiting for her son and speaks of him in the present tense. Each Sunday, she goes to Mass to pray for his return.

“I always speak to God,” said Ms. Ramos. “I am always looking up at that picture of the Virgin. I am scared one day she will yell back at me, ‘Enough, already. That’s enough.’”

Whims of the Passage

Rolando Bello sat on a pier in Curaçao, worrying about his mother. It was September, a week before she stepped aboard a boat to join him in Curaçao. He knew the dangers well, having made the journey twice himself.

Last year, he says, Mr. Cordero and Mr. Ramos had approached him to join their doomed trip before they set off.

“I was this close to going,” he said. “You see what would have happened to me.”

Now his family was being subjected to the dangerous whims of the passage once more.

His mother’s boat was getting ready to set off. His sister, who had been dragged ashore by her hair, had been caught by the Curaçao authorities and deported back to Venezuela over the summer. Desperate to work, she had sneaked into Aruba instead, taking a loan from a smuggling ring to get there.

But at least his wife was with him. She came to Curaçao that month under a new scheme. Because she did not have the $1,000 needed to pose as a Venezuelan tourist at customs, smugglers rented her the money to satisfy the new cash requirement, which is imposed only on Venezuelans. The smuggler’s agents in Curaçao then quickly approached her at the airport to take back the money — and to collect the $100 rental fee.

Mr. Bello’s wife, Lennymar Chávez, sat next to her husband and the two ate a large lunch. A boat sailed past a row of colonial facades, and Venezuela felt a world away.

“I haven’t eaten an arepa for three months,” she said, referring to the Venezuelan staple of corn flour, which has become increasingly hard to find at home. “I ate one here in Curaçao for the first time.”

They had left their 7-year-old daughter in La Vela with relatives. Mr. Bello had trained to be an engineer in Venezuela’s oil industry. Now he was a construction day laborer, happily earning about $65 a day. Ms. Chávez trained to be a nurse, but held few hopes of working in her profession in Curaçao.

“I don’t mind cleaning now,” she said. “The important thing is that I’m working here.”

But the authorities in Curaçao, like many tiny islands, fear the immigrants will undercut the local labor force or bring violent crime.

“My preoccupation is what kind of people are entering Curaçao,” said Nelson Navarro, the island’s justice minister who argued that the increase in Venezuelans coincided with a 15 percent rise in crime, particularly armed robberies. “In Venezuela, they don’t hesitate to shoot a police officer, but here, this is news.”

Alex Rosaria, a legislator on the island, worries that the migrants will further strain Curaçao, where unemployment is at 11 percent.

“We have only a limited capacity to deal with refugees,” Mr. Rosaria said.

For now, the task has been left to the Dutch Caribbean Coast Guard. Rob Jurriansen, a Dutch naval officer who heads operations in Curaçao, says his small fleet intercepted only a tiny fraction of the migrants, perhaps just 5 percent to 10 percent of the illegal immigrants arriving in Aruba, Bonaire and Curaçao, the islands the fleet patrols.

Now, he says, officials in the Netherlands, the former colonial power that is still formally tied to Curaçao within the Kingdom of the Netherlands, fear they will also get stuck with the bill of caring for a migrant tide.