Gateway International Bridge is one of three bridges across the Rio Grande between the Mexican city of Matamoros and Brownsville, Texas, that form a metropolis spanning two countries.

Southbound, cars and people trickle virtually unimpeded into Mexico. Northbound, cars line up bumper to bumper while crowds of pedestrians snake along the sidewalk to join the queue for the US port of entry. On this sidewalk, at the Mexico end of the bridge, is a cluster of visibly frazzled refugees, some with folding chairs and tables and others lying on thin rugs on the ground, sheltering in the shadow cast by a nearby customs building.

Miguel, a Cuban in his late 20s, has been waiting on the bridge for almost a week.

“It makes me stressed to wait so long,” he said. “We’ve been waiting here for six days. I’ve caught a cold, too … we wait even when it rains.”

Miguel is one of a new class of asylum seekers who are stuck in limbo – literally suspended between two countries, neither of which wants to accept them. Their predicament is the result of a change in how US border agents treat asylum seekers, one that goes hand in hand with the Trump administration’s zero-tolerance policy – the subject of a major Guardian investigation this week. The result is a catch-22 for 21st-century refugees who reach the doorstep of America and are faced with two bad choices: get stuck in no man’s land trying to enter the US legally, or risk being criminalized trying to set foot on US territory.

A woman from Honduras camps on the bridge with her family. Photograph: The Washington Post/Getty Images

Asylum is a protection granted to foreign nationals who have fled their home countries, fearing persecution. If asylum is granted, it allows migrants to stay and work in the US and creates a pathway to citizenship.

Before this summer, asylum-seeking migrants arriving at the border were allowed into the immigration building on the American side of the bridge. Because the building is on US soil, they couldn’t legally be turned back into Mexico. Since May, however, border agents have started blocking those without a US passport or visa from passing the middle of the international bridges. This means they can’t set foot on US territory, nor can they stay in Mexico once their two-week transit visa, granted to those heading through Mexico to the US, expires.

Instead they put their name and position in the queue down on a list kept by the Mexican authorities, and camp out on the bridge until US border agents say they have capacity to process them.

I’m not a beggar. I’ve had to leave my country to try for a better life. I still have my dignity. Agustin, Cuban asylum seeker

Miguel, from Cuba’s Granma province, fled his country out of fear. “I’m not in agreement with Cuba’s politics. I’ve been beaten up by the police,” he said.

When the Guardian visited the bridge on a single day in mid-September, Miguel was sitting among a group of 10 Cuban refugees. Some charged their phones from an extension cord attached to a Mexican government building; others rested as they waited for officials to call their turn.

“It’s not a zoo,” said Jhonny, an athletic twentysomething, gesturing towards the steady stream of Mexicans walking past.

“People stare and take photos of us,” he added, noting that “some people also offer us food.”

Barbara, 50, has been waiting the longest: 12 days. “I have hypertension and I had to be hospitalized the other day. I don’t like living outside. Fortunately, I did not lose my place in the line.”

After almost 11 days, Jhonny is getting impatient.

Some asylum seekers have been waiting more than a week. Photograph: Alamy Stock Photo

“They give preference to old people or pregnant women,” he said. “Yes we’re frustrated, but what can you do?”

Agustín, who is traveling with his 21-year-old daughter, Danay, tries to remain optimistic.

“People offer us money while we wait because they see us sat on the ground and think we are beggars,” he said. “But I’m not a beggar. I don’t agree with Cuba’s politics. I’ve had to leave my country to try for a better life. I still have my dignity.”

Some experts question the government’s logic of making it so onerous for refugees to request their human right to asylum.

We are treating asylum seekers with disdain Everard Meade, Trans-Border Institute director

“We are treating asylum seekers with disdain,” said Everard Meade, the director of the Trans-Border Institute at the University of San Diego in California. “The whole architecture of enforcement is designed to prevent people who might have a valid asylum claim from being able to make them because the US makes it so difficult to get here.”

The US attorney general, Jeff Sessions, has made it clear that the government will create “extreme negative incentives” for people who try to enter the US unlawfully, Meade said.

“And what happens when people follow the law? They can’t get into the port of entry to make their claim. It makes it seem like the administration is talking out of both sides of their mouth at once and it seems incredibly hypocritical.”

Some experts believe making asylum seekers wait on bridges has unintended legal consequences.

“Instead of waiting, they cross unlawfully and that exposes them to prosecution,” said the lawyer Carlos Spector, who has worked on political asylum cases for the past 30 years in El Paso, Texas.

The backlog shows no signs of easing.

“Yesterday they took in two people. The day before that they took in three people,” said a Mexican immigration official watching over the bridge. “Today they haven’t taken in anybody.”