The moving story of an immigrant about her arrival in the US 2:21
(CNN) --
As freezing temperatures hit El Paso, Texas, some immigrants who have not turned themselves in to Customs and Border Protection (CBP) are having difficulty finding shelter.
Three men, who did not want to be named, told CNN that they have been expelled from the United States multiple times in recent weeks.
They said they no longer wanted to turn themselves in to border authorities because they have been denied legal entry too many times.
The men claimed they crossed the river and through border barriers without being detected by agents.
El Paso has opened government-run shelters at the convention center, in hotels and at several disused schools, but cannot accept immigrants without CBP documentation, El Paso city spokeswoman Laura Cruz Acosta said. .
The city must follow state and federal policies that supposedly say immigrants must have the required documentation in order to receive shelter in government-run facilities, he added.
If undocumented immigrants show up at government-run locations, they will be put in contact with CBP to start the handover process or put in touch with NGO-run shelters on the ground, he explained.
Immigrants without documentation have few accommodation options, but some NGOs accept them at their facilities.
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CNN spoke to two shelters that accept undocumented immigrants but are overcrowded.
Overcrowded shelters in El Paso fear for immigrants
John Martin, deputy director of the Opportunity Center for the Homeless, told CNN he has asked the city's emergency department to open the convention center to undocumented immigrants for at least the next two days, but has been unsuccessful, he said.
On Wednesday night, more than 290 men slept in a men's shelter run by his organization, despite the space being designed for just 125 people.
"We are literally forced to close our doors tonight," he said.
"We just can't accommodate anyone else."
In the nearby church of the Sacred Heart, those responsible explained that its normal capacity is 130 people, but that they are going to expand it to 200 during the next four nights and that they are giving priority to women and children.
But hundreds of people are still waiting outside the church.
"My biggest fear is that someone won't wake up tomorrow morning," Martin told CNN.
"I hope to be wrong".