Mr. Trump has said he will choose as his nominee for attorney general Senator Jeff Sessions, Republican of Alabama, a vigorous proponent of strong immigration enforcement. With broad powers over the immigration courts, Mr. Sessions could appoint tough judges and change procedures so the system in the future would move faster and be more restrictive.

Mr. Sessions could cancel the appointments of roughly 75 new judges selected by Attorney General Loretta Lynch to choose judges to his liking. But it might be a year or longer before they took the bench. And Mr. Sessions would not have authority to summarily reduce the backlogs, lawyers said.

As the backlogs grow, they create new problems. People who come to the courts with urgent stories of terrifying dangers that drove them from their homes find they cannot be heard for years. Circumstances change, evidence grows old, witnesses move on. Cases get scrambled or misplaced.

When Reina Rojas de Ayala first filed for asylum in Arlington in 2012, she had a strong argument that she would be in grave danger if she was forced to return to El Salvador. By the time she had a hearing four years later, her legal case was diminished even though the perils at home were not.

Ms. Ayala, 43, lived in Virginia with her Salvadoran husband, a legal immigrant. But she was undocumented, and in 2009 she went to El Salvador to try to obtain papers to return legally, taking two children born in the United States.

The danger came from one of her older sons in El Salvador, Samuel Ayala, now 26. He demanded money, saying he needed to pay dues to a criminal gang.

“He was violent, telling me he had to have the cash,” Ms. Ayala said. “I told him to get a job. Many times he shoved me down and hit me.” Fearing he would kill her, she sent her American children to Virginia by plane while she went to the border to request asylum.