Lawsuits claiming Wells Fargo, Navient, and others unlawfully tried to get borrowers to repay private student loans even though the obligation was wiped out in bankruptcy are moving through the courts with key arguments and rulings expected in coming months.

There are four proposed class action cases in all with attorneys, banks, judges, and other stakeholders keeping an especially close eye on the U.S. Court of Appeals for the Fifth Circuit in Texas.

That’s where a panel of three judges...