The New York Times reports in "In New Jersey Student Loan Program, Even Death May Not Bring a Reprieve," that the state of New Jersey wants its money back because it does not forgive loans when debtor-students pass away. That often means parents who have cosigned the loans are required to pay them off.
Most private student loans issued through banks operate in the same way. The loan must still be paid after the student debtor passes away. If there is not enough money in the estate to cover the costs, cosigners are stuck with the bill.
On the other hand, loans insured by the federal government are written off if the debtor passes away. It is not automatic, however. Executors need to take affirmative steps to have the loans forgiven, but it is not a difficult process.
An estate planning attorney can guide you in dealing with unpaid student loans and the proper way to handle them in an estate.
Reference: New York Times (July 3, 2016) "In New Jersey Student Loan Program, Even Death May Not Bring a Reprieve"