REYNOSA, Mexico — This city has become so dangerous for migrants that the nuns at a migrant shelter in Reynosa have had to establish a new rule: No one can leave the compound.

“They walk outside to get a sandwich, and they disappear,” Sister Edith Garrido said.

Over the past several years, migrants have increasingly been targeted by criminal groups in Reynosa and other cities along this stretch of Mexico’s border with the United States. They have been kidnapped after withdrawing money. They have been pulled off buses by armed men. Shootouts have occurred so close to the migrant shelter that nuns have found bullets on the floor.

And now, with Thursday’s announcement by the United States that it will force asylum seekers to wait in Mexico as their claims are processed, Reynosa might soon be home to hundreds or thousands of migrants waiting to seek refuge in the United States. No one is sure how they would survive here.

In 2018, the United States received more than 100,000 asylum applications. The government hasn’t said how many of those applicants traveled through Reynosa or the other dangerous border towns in the state of Tamaulipas. But almost any surge in migrants here could have devastating consequences. The state says its five migrant shelters have the capacity to house only 600 people at the same time.

Already in Reynosa, its two shelters are sometimes so overwhelmed with recent deportees that migrants sleep on the floors of kitchens and hallways. Those who can’t find space at a shelter put themselves in great peril. State immigration authorities say migrants are consistently picked off by organized criminals, sometimes held for as much as $5,000 ransom and sometimes forcibly recruited by cartels.

“They are targeted because they are vulnerable, because they are seen as an easy source of money,” said Ricardo Calderón, the top immigration official in Tamaulipas.

Violence in Tamaulipas skyrocketed beginning in 2009 as the federal government sent in the military to confront the state’s drug cartels. But the cartels ended up splintering, fighting both one another and security forces. In some cases, organized-crime offshoots focused more on kidnapping than on drug trafficking.

In 2010, 72 migrants were killed about 90 miles south of here, in the ranches of San Fernando. Police found their decomposed bodies and later accused the Los Zetas cartel of the killings.

There are no reliable government statistics on how many migrants have been kidnapped, killed or extorted in Reynosa, though the reports are frequent. In October, Mexican authorities found that 22 migrants, mostly Hondurans, had been kidnapped here.

Each week, the nuns at the Casa del Migrante receive phone calls from families in Central America looking for their missing relatives. At least once in recent months, Calderón said, armed men forced migrants off a private bus heading out of the city.

The Mexican government said Thursday that it would grant work permits to the migrants who wait for their asylum processes to unfold in the United States and that it would ensure they have access to legal services.

But few American lawyers are willing to travel regularly to cities such as Reynosa. And the idea that migrants could spend months or years working here while awaiting an American judge’s decision is baffling to immigration experts and local officials.

“Under international law, you can’t send someone back to a dangerous place, you can’t send them back to cartel country,” said Jennifer Harbury, an immigration lawyer based in McAllen, Tex., and one of few who works in Tamaulipas. “How would you even get a lawyer to talk to you?”

U.S. officials suggested Thursday that if asylum seekers could prove their fear of persecution in Mexico, they could avoid being returned to cities like Reynosa. But it remains unclear what kind of proof would be necessary.

“Mexico can say welcome and we’ll give you work and provide safe haven, but there are no safe havens in these places,” Harbury said.