After his college graduation, the high school where he had been a standout science student asked him to come back as a teacher. At the MAST Academy in Key Biscayne, a magnet school that draws science students from across the Miami area, he is earning a steady official paycheck, with his tax withholding in order. And he is loving his work.

“This is a very nerdy school where the kids are encouraged to be curious,” Mr. Péndola said in his laboratory after an advanced chemistry class. “I like being able to excite them about chemistry, which is not normally everyone’s favorite subject.”

Nearly 640,000 young immigrants have received protection since 2012. As many as 270,000 others could be eligible under the new rules. The immigrants, most of whom came with parents and either crossed the border illegally or overstayed legal visas, receive temporary work authorization but no lasting legal immigration status.

Ms. Benítez, who has lived in the United States since she was 13, is now 36. She was too old in 2012 for the age limit of 30 in the program. Under the expansion, Mr. Obama eliminated that age cap. He also reset the date by which applicants must have been in the United States from June 2007 to January 2010 and extended the term of the deportation deferrals from two years to three.

Ms. Benítez’s mother is a legal resident, and several siblings are American citizens. In 2004 she applied through the legal system for a resident green card, but because of vast backlogs she still has many years to wait.

With a 10-year-old daughter who is a citizen, Ms. Benítez would also be eligible for the other program the court order suspended, for as many as four million undocumented parents of citizens or legal residents. It had been scheduled to begin in May.