For years, Michael Shahbazi’s phone has often rung numerous times a day with calls from the nation’s largest educational loan servicing company, Navient, pressing him for payments on his student loan. In 2011, Mr. Shahbazi filed for bankruptcy, and yet still the calls continued. Navient has also called his family members, including his mother-in-law and brother, and his wife’s employer.

But on April 25, those calls will cease—not only for Mr. Shahbazi, but for about 16,000 other student loan borrowers like him who’ve declared bankruptcy, and whom Navient has pursued with similarly aggressive tactics.

Navient made the change in response to a motion for preliminary injunction and limited class certification in a lawsuit filed by Mr. Shahbazi and Evan Brian Haas, another student borrower, in US Bankruptcy Court in the Southern District of Texas. The case is Evan Brian Haas, Michael Shahbazi, et al. v. Navient Solutions, LLC and Navient Credit Finance Corporation.

Representing Mr. Shahbazi and Mr. Haas in the case are the New Orleans-based law firms of Jones Swanson and Fishman Haygood, as well as New York-based Austin Smith, Chicago-based Joshua Kons, and Houston-based Adam Corral and Marc Myers. On May 11, the firms were appointed interim class counsel and interim lead counsel for absent class members.

Under the terms of the voluntary agreement that Navient filed with the court, the company will no longer phone or otherwise contact borrowers with certain student loans who filed for bankruptcy after October 2005. Instead, it will simply send them monthly statements.

Jones Swanson and co-counsel will send out correspondence in May and June to alert student loan borrowers who qualify as potential class members about these changes in Navient’s collection methods.

Navient’s agreement is just the latest step in a long, contentious history of student loans and the rules concerning their repayment.

In the 1970s, Congress changed the bankruptcy code so that it became nearly impossible for borrowers to discharge most types of student loans, even as part of a bankruptcy proceeding.

Since the 1970s, however, private financial institutions have broadened the definition of what they offer as “educational” loans, including those intended to pay for unaccredited programs like career training and bar-exam study.

In 2014, one of the attorneys on Mr. Shahbazi’s and Mr. Haas’s case, Austin Smith, wrote an article in Consumer Bankruptcy, a newsletter published by the American Bankruptcy Institute, in which he proposed that some of these loans did not meet the bankruptcy code’s requirements for educational loans. Therefore, Mr. Smith wrote, they were dischargeable. In March 2016, he made the same argument in court, and prevailed.

Now Mr. Shahbazi’s and Mr. Haas’s case against Navient could test this argument for the first time as a class action.

“I have yet to go in front of a judge who disagrees with my overall thesis, which is that not all student loans are not dischargeable,” Mr. Smith recently told MarketWatch. “I do think the tide is now turning on that.”