Ms. Benítez graduated from the University of Wisconsin-Milwaukee, with an engineering degree. But she has been clinging to a job as a quality control manager on a castings production line, relying on car pools to get to work and keeping quiet about her legal status.

“You can’t show your face because you are holding on to the one job that will feed your family,” she said.

She hired a lawyer and assembled years of tax returns and bills for her application, laying plans to get a data job and apply to graduate school. Then she heard the news of the injunction.

“I was really raging,” she said. “Now I’m just numb.”