ARTESIA, N.M. — Sitting before a small video screen in a bare room in a remote corner of New Mexico, a young Honduran woman told her story this week to an immigration judge in Virginia. She had been serially raped, she said, spat upon and relentlessly hounded by a drug-dealing husband who regarded her as his property.

“I felt a fear of him so terrible it’s difficult to explain,” the woman, Heidy Lara Carballo, told the judge in a hearing on Thursday. When she last saw her husband before she fled to the United States, she said, he was circling their house, firing shots into the air, as she tried to hide inside.

“If I go back to Honduras, it is certain death,” Ms. Lara Carballo said.

The judge agreed, and in the first case to be decided since this center opened in June, she granted Ms. Lara Carballo’s request for asylum, saying she had presented a “textbook case” for being allowed to stay in the United States.

Ms. Lara Carballo’s case and others being heard here are changing the nature and purpose of a temporary detention center that the Obama administration set up in windowless barracks behind high fences for women and children caught crossing the border illegally. The plan was to hold the detainees briefly until they could be deported, sending a message to Central American families that illegal migrants would not be allowed to stay.