El Paso, Texas — Prayer is paramount at the Annunciation House, a network of shelters in this Texas border city that has been housing and feeding destitute migrants for nearly half a century.

At one of the Catholic charity's shelters, several migrants, most of them families with children, huddled for a prayer before enjoying hearty meals cooked by a group of American volunteers. The hungry migrants thanked God for the food, and prayed for those still trying to reach the U.S.

Leading the prayer was Ruben Garcia, who founded the Annunciation House in 1978 and continues to run it as its director. 

"We come from a Catholic tradition. But this isn't Catholic. This isn't Lutheran. This isn't Episcopalian or Methodist or Presbyterian. This is Christian. It is Jewish. It is Muslim," Garcia told CBS News. "Constitutive to each of those faith traditions is 'I was a stranger and you welcomed me.'"

For many migrants entering the U.S. near El Paso, historically one of the busiest migration corridors along the southern border, the Annunciation House is the first stop to get hot food, a change of clothes, showers and a place to sleep before they arrange travel to their final destinations, which tend to be major American cities.

Throughout its decades-old history, the Annunciation House has received tens of thousands of migrants, giving needy newcomers a lifeline in the U.S. and helping Border Patrol agents prevent dangerous overcrowding in government facilities during spikes in illegal border crossings that have bedeviled Republican and Democratic presidents alike.

But in an era of deeping political polarization over U.S. immigration policy, the Annunciation House now finds itself at the center of a legal fight with the state of Texas that could lead to closure of the faith-based organization.

A "stash house"

That legal battle started in February, when the office of Texas Attorney General Ken Paxton demanded documents from Annunciation House as part of an investigation into the nonprofit, saying shelter officials would be breaking the law if they refused to comply.

The Annunciation House filed a lawsuit asking a state judge to pause Texas' documents demand while it reviewed the matter. That request was granted. But Paxton's office then asked the same judge to shut down Annunciation House's operations all together, accusing the charity of violating state laws.

"Annunciation House is engaged in systematic conduct that constitutes illegal alien harboring and operation of a stash house, as a matter of law — both of which constitute felony offenses under the Texas Penal Code," Paxton's office said in a legal filing.

Paxton's office revealed it had been surveilling the Annunciation House as part of a broader effort to enforce a directive by Texas Gov. Greg Abbott that called for investigations into organizations helping migrants. Under the Biden administration, which has faced record levels of unlawful border crossings, Republican lawmakers in Washington and across the country have accused nongovernmental groups of encouraging illegal immigration by sheltering and feeding migrants.

In their legal filings, Texas officials said the Annunciation House has helped not only migrants released by federal immigration agents, but also those who entered the country illegally without being processed.

Earlier this month, state Judge Francisco Dominguez denied Texas' request to shut down Annunciation House and imposed requirements on any future documents requests from Paxton's office. In a scathing order, Dominguez denounced Paxton's documents demand as a "pretext to justify its harassment of Annunciation House employees and the persons seeking refuge." 

Texas officials, Dominguez added in his order, did not initially disclose they were probing the charity for alleged criminal conduct. "This is outrageous and intolerable," he wrote.

Paxton's office notified Dominguez last week it is appealing his orders to the Texas Supreme Court. It did not respond to multiple interview requests or questions, including about how many migrant services organizations it is investigating. 

According to court records, the Texas attorney general is also investigating the Catholic Charities of the Rio Grande Valley, one of the main organizations sheltering migrants in the region. A judge recently denied Texas' bid to depose a representative of the group who has knowledge of its alleged role in "facilitating alien crossings over the Texas-Mexico border."

The Catholic Charities of the Rio Grande Valley has called Texas' effort a "phishing expedition," noting it has provided documents to Paxton's office. In a statement to CBS News, the charity said it offers "services to immigrants within the letter and spirit of all laws."

"We will always strive to fulfill our legal obligations while continuing to steadfastly pursue our mission, inspired by Sacred Scripture and the Social Teaching of the Catholic Church," the nonprofit added.

"I think it's happening because of the politics"

Garcia, the Annunciation House's director, has maintained his organization is simply helping desperate people in need.

"The state of Texas has no reason to want to come after an NGO whose entire history has been dedicated to human rights. I think it's happening because of the politics," Garcia said. 

If Texas is successful in its bid to close down the Annunciation House, migrants like Wilson Juárez Hernández could be left in limbo. The 22-year-old from Guatemala has been living at one of the Annunciation House shelters since surviving a fire at a Mexican immigration detention center in Ciudad Juárez that killed 40 migrants last year.

"Many friends, many young people around my age died," Juárez Hernández told CBS News in Spanish. 

While he and other migrants survived, he noted, "not all of us left unscathed."

The smoke Juárez Hernández inhaled from the inferno disabled him, forcing him to use a wheelchair. He was allowed into the U.S. to undergo medical treatment. For some time, he could not eat, bathe or dress himself without help from others. With no family in America, Juárez Hernández has nowhere to go in the U.S. if Texas closes the Annunciation House, which is paying for his physical therapy and medical expenses.

While it is still unclear if he will be able to walk again, Juárez Hernández has slowly learned to do most basic activities, from eating and getting dressed, by himself. He's also learning English, and still dreams of becoming a doctor, a dream he said he's had since he was 10 years old.

"Happy," he said, is his favorite word in English so far. Asked why,  Juárez Hernández said, "because I'm always happy."