Ms. Bueso and others had received letters in August from the agency, which adjudicates immigration benefits, notifying them that their requests to remain in the country had been denied. That drew criticism from lawyers, Democratic lawmakers and doctors, who said their patients were being issued a death sentence.

A few weeks later, the government said it would reopen the cases of those who had received denials, sending them letters to that effect. However, it did not tell them whether their requests had been granted or clarify how other applicants should proceed. It said only that cases would be considered by another agency, Immigration and Customs Enforcement. But that agency, which oversees deportations, told The New York Times that it had not been consulted and was not prepared to take on the role.

Representative Ayanna S. Pressley, Democrat of Massachusetts, sponsored a letter signed by more than 120 members of Congress demanding answers from homeland security. She then called for an emergency oversight hearing about the elimination of the program.

On Thursday, Michael Anderson, president of Benioff Children’s Hospital at the University of California, San Francisco, where Ms. Bueso receives weekly treatment, said, “We hope this will apply to every patient who requires lifesaving care, including our patient Isabel Bueso and other children in her situation.”

Ms. Bueso, who has an enzyme disease that causes dwarfism and other physical deformities, has remained in the country since she was 7 to receive treatment and participate in additional medical studies; she has renewed her deferred action status every two years. Her parents pay for private health insurance to cover her care.