EL PASO, Texas—“This administration did not create a policy of separating families at the border,” Homeland Security Secretary Kirstjen Nielsen said from the White House on Monday.

Tell that to Donelda, 35, and her daughter, 6. Both are asylum seekers from Guatemala who were turned away by U.S. Customers and Border Patrol at the Paso del Norte port of entry on May 8, the day after Attorney General Jeff Sessions announced the Trump administration’s new “zero tolerance” immigration policy. (The Daily Beast is withholding Donelda’s surname and her daughter’s name to protect them from feared retribution for speaking.)

Like others who have been turned away since then, Donelda then tried to cross into the United States illegally, turning herself into Border Patrol. That’s when—under the new policy—she was prosecuted criminally and her daughter was taken from her and shipped to a detention center in the Midwest, thousands of miles away.

“If I had known I’d be separated from my child, I wouldn’t have come,” Donelda said through her attorney in El Paso, Iliana Holguin.

Donelda’s statement may be exactly why the Trump administration launched zero tolerance: to prevent people with children from even thinking about coming to the United States.

“How low are we willing to go as a society to deter people from coming to the U.S.?” Holguin told The Daily Beast. “It is a deterrent, but is that who we want to become?”

For the past several weeks, as thousands of migrant children have been taken away from their parents, Nielsen has said migrants seeking asylum at ports of entry will not be prosecuted or have their children taken away from them.

“If you’re seeking asylum, go to a port of entry,” she said Monday. “You do not need to break United States law to seek asylum.”

Left unsaid is the fact that border agents are making it difficult for migrants to apply for asylum, practically daring them to cross illegally.

Neilsen’s office declined to respond to a request for comment. The White House did not respond to a request for comment.

Even when migrants know that they must specifically say they’re applying for asylum, border agents are turning them away at points of entry like Paso del Norte, saying there is “no room” in holding cells there. Some of those migrants, like Donelda, wait in a levee between El Paso and Juarez for border agents to arrest them, multiple immigration attorneys and advocates in El Paso told The Daily Beast. Once in custody, migrants are charged in criminal court with illegally crossing the border. After they plead guilty, they are placed in ICE custody where they can apply for asylum.

Since Sessions announced the policy last month, more than 50,000 people have been arrested as part of the zero tolerance push, resulting in more than 2,000 children separated from their parents.

Donelda’s daughter has been returned to a facility in El Paso, and the child’s advocate in the Midwest is hopeful that she and her mother will be sent back to Guatemala together.

“The law doesn’t say you only accept applicants for asylum if there’s space at your facility,”  Holguin said. “What the government is trying to do is stop that physical entry by putting agents in the middle of the bridge.”

CBP said it was taking a “proactive approach to ensure that arriving travelers have valid entry documents in order to expedite the processing of lawful travel,” in a statement.

“Depending upon port circumstances at the time of arrival, individuals presenting without documents may need to wait in Mexico as CBP officers work to process those already within our facilities,” the statement said.

For some, waiting in Mexico means sleeping on the streets of Juarez and begging for food for their children.

Donelda isn’t the only one who was denied asylum simply because she didn’t say the word “asylum.”

For three days last week, a grandmother fleeing with her family from criminals who have taken over her village tried and failed to apply for asylum at Paso del Norte. Dejected, she cried on Saturday when she reached her daughter in her village in the southern Mexican state of Guerrero by phone.

“I’m very sick,” she said, noting her arthritis and her difficulty walking. “If I go back home and they kill me, they kill me. But my granddaughter made it across, and that’s the important part.”

On the first day, she and her family were turned back when border agents told them there was no room in holding cells for asylum seekers. They were turned away again the next day, echoing stories of others who have been prevented from seeking asylum.

“They say there’s no room, but that’s ridiculous. They made more room at Tornillo,” said Alan Dicker of the Detained Migrant Solidarity Committee, referring to the Tornillo port of entry not far from El Paso that will be home to a new facility that will hold hundreds of migrant children. “So what’s the alternative? The alternative is that they’re homeless in Juarez.”

Finally, on Friday, Dicker and other advocates argued with border agents until the family was allowed to pass and apply for asylum.

“The only way to do it is to bully the border agent folks to let them in,” Holguin said.

Holguin said agents have said their actions were a result of orders from “on high.”

Holguin and others claim border agents are violating both U.S. and international law by blocking asylum seekers. Migrant advocates in El Paso and elsewhere are training volunteers to monitor points of entry for turnbacks and confront agents by telling them the law requires them to allow asylum seekers to pass.

The two bridges at Paso del Norte, which spit out into El Paso on Santa Fe and Stanton streets, are filled each day with thousands of people crossing the border. Once on the U.S. side, travelers must present their passports and visas to be allowed through—or apply for asylum.

This can only happen if migrants are able to reach the facilities on the U.S. side of the border. With such large numbers of people on the bridge, it can difficult to distinguish travelers with valid visas from those seeking asylum. But the border agents have found a way.

“They racially profile them,” Dicker said. “If you look like you’re from South or Central America—anywhere other than Mexico—they’ll stop you and tell you there’s no room.”

CBP and DHS did not respond to a request for comment on the turnbacks at Paso del Norte. ICE responded to questions about Donelda with a statement about a completely different Guatemalan woman who was arrested on May 10 in Yuma, Arizona.

Many of the asylum seekers are fleeing “failed states” in Central and South America, Dicker said. The Juarez side of Paso del Norte is at times a rainbow of Guatemalans, Nicaraguans, Salvadorans, and Brazilians who are fleeing violence-plagued neighborhoods in their home countries.

Early Friday morning, Dicker and others were successful in getting the grandmother and her family past agents and into processing. He thought that was the end of it until he spotted the grandmother on the bridge Saturday afternoon, alone. After being separated from her granddaughter and great-grandchildren, the woman was told she could either apply for a U.S. visa while in ICE custody or return to Juarez. The granddaughter and her children are now in a detention facility waiting for their asylum case to be heard.

Eventually, Dicker reached the grandmother’s contact in Juarez. Holding her hand, the two crossed the street and walked back into the city. There, Dicker had her sign a declaration he’d written containing the details of her story. It might be part of an eventual lawsuit against border agents who may be in violation of U.S. law by not allowing migrants to apply for asylum. Maybe it will be just one small act of documentation in the never-ending work of advocates working on behalf of migrants every day here.

“I just don’t want to be alone,” the grandmother said, crying as she finally reached her daughter by phone in a small village, some 1,300 miles away.