Backed by one of the nation’s biggest unions, nine teachers filed a lawsuit on Wednesday accusing the student loan servicer Navient of negligently blocking their access to a troubled federal loan forgiveness program for public service workers, adding thousands of extra dollars to their debts.

The lawsuit, which is seeking to become a class action, was filed less than a week after a government audit report detailed extensive problems with the loan forgiveness program. In the year since the Education Department began accepting loan discharge applications, it has rejected more than 99 percent of them. Nearly 28,000 sought relief, but only 96 borrowers received it, according to the audit.

To qualify, borrowers must work for government or certain nonprofit employers for at least 10 years, have the right kind of federal loan (a “direct” loan) and have made 120 monthly payments on it through a specific type of payment plan. Servicers like Navient are supposed to guide people through all of those hoops.

Instead, Navient gave inaccurate information to borrowers who sought help joining the program, and discouraged them from taking steps necessary to qualify, according to the lawsuit, which was filed in federal court in Manhattan.