Existing rules allow students to apply for a loan release if they attended a college that broke state laws. But that process, once used very rarely, has been overwhelmed with claims after a wave of failures by for-profit institutions. Some students have had applications pending for years.

Borrower advocates say the system came to a halt in the first few months of the Trump administration. The gears are turning again, according to the Education Department — but only for a fraction of those who are waiting.

In January, one week before President Trump took office, the Obama administration said 23,000 applicants had been notified that their claims had been approved. Nearly 7,000 of those claims have been discharged, and the rest will be soon, according to Elizabeth Hill, a department spokeswoman.

But the Obama administration also said in January that it had 68,000 applications awaiting further review, on which no decision had been made. Those cases “will still be reviewed under current statute,” Ms. Hill said.

Borrowers caught in the pipeline say that they have been given no information about why the decisions are taking so long. A coalition of 31 military and veterans groups sent a letter to Congress and Ms. DeVos this week stating that “veterans’ applications for relief remain stalled.”

Last week, a federal court judge in California ordered the Education Department to file a report within 90 days on one borrower’s application that has been under review for more than two years.

Another borrower, Victoria Linssen, applied in October for forgiveness on the $50,000 in federal loans that she had taken out to study photography at the Brooks Institute in Ventura, Calif., a for-profit college that shut down last year after extensive regulatory criticism and penalties. The college lied about its accreditation, its job placement rate and the wages its graduates earned, Ms. Linssen said.