It is a common occurrence: an undocumented immigrant gets pulled over for a traffic violation, ends up in detention and swiftly is removed from the United States. In the case of Tania Romero, a Honduran mother of four who was arrested recently in Georgia, a deportation could happen within days.

But her case is not so common. Ms. Romero has been receiving treatment for Stage 4 oral cancer that needs continual attention. And she has a son, a doctoral student at Yale University who is himself undocumented, who was not about to stand idly by.

“I grew up in this country. My mother is the single biggest reason I am at a school like Yale,” her son, Cristian Padilla Romero, said of the public campaign he started to win his mother’s freedom.

“She guided me, worked three jobs to support me,” said Mr. Padilla Romero, 24, who was 7 years old when he came to the United States.