Students who take out private loans to pay for college could face a nasty surprise if their co-signer dies or files for bankruptcy: The lender may suddenly demand the loan be paid in full—or even worse, put that loan in default—even though all payments are being made on time.

SallieMae buildings in Reston, Virginia.

The Consumer Financial Protection Bureau issued a consumer advisory on Tuesday, warning borrowers that these "auto-default" clauses may be in their loan agreements and serious financial consequences could result.