Private student lenders are promising not to trigger defaults of new student loans when co-signers die, said the Consumer Financial Protection Bureau’s director Richard Cordray on Thursday.

Cordray called the change a welcome move to make student loans safer, but cautioned that these “auto-defaults” on the death of a co-signing parent or grandparent for existing loans is still possible.

He said strengthening protection for these young borrowers is key because the loans are major early steps for them to establish creditworthiness. Their success or failure at paying off college loans can have a major impact on their financial lives for years to come.

Looking broadly at consumer loans, Cordray said the CFPB still has much to do to improve practices among a wide range of lenders—from credit card issuers to those who make auto loans—because borrowers often have no recourse when things go wrong.

His remarks came in a prepared speech for the bureau’s Consumer Advisory Board.