Ms. Rayos was 14 when she left Acambaro, a city in an impoverished corner of the Mexican state of Guanajuato, and sneaked across the border into Nogales, Ariz., a three-hour drive from Phoenix. She married — her husband is also undocumented, and thus did not want his name published — and gave birth to a boy and a girl, who are now in their teens.

Ms. Rayos was working at Golfland Sunsplash in Mesa, a suburb of Phoenix, when Maricopa County sheriff’s deputies swooped in on Dec. 16, 2008, arresting her and several other employees on charges of suspicion of identity theft and using forged documents to obtain employment. The raid was one of the first ordered by Joe Arpaio, who was sheriff at the time, under an Arizona law authorizing sanctions against employers who knowingly hired undocumented immigrants.

She spent three months in a county jail, followed by three months in immigration detention, she told a reporter. In 2013, an immigration court ordered that she be sent back to Mexico, but her case had been on hold since the federal authorities — under the Obama administration — decided not to act on the deportation order.

Her son, Angel, still remembers the evening of her arrest — the knock on the door, the flashlight on the darkened living room, the sight of handcuffs on his mother’s wrists.

“I was in second grade,” he said. “I never forgot that night, and I’ve lived in fear of losing my mother every night since then.”

Ms. Rayos was afraid to go to her appointment on Wednesday, knowing what might happen. Carlos Garcia, executive director of Puente, an immigrants’ rights group, told her she could skip it and go into hiding or seek refuge at a church in North Phoenix, joining two other unauthorized immigrants facing deportation who have lived there for months.

She decided to face the odds. Before her appointment, Ms. Rayos and her family attended Mass. Later, she stopped for a moment, clasped her hands and bowed her head, as if she were reciting a silent prayer.