I am sorry to hear about your loss. Our thoughts and prayers are with you and your family.
Officially, I don't know. But, when our son died it didn't happen. Our son died with outstanding student loans and his estate received a tax refund from his final tax return. Since our son was the only one who signed the student load agreements, and there was no money left in the estate after funeral expenses and even after the tax refund, the loans died with him.
Unless you (or someone else) co-signed for the student loans, no one has an obligation to pay them. In fact, if your son was single when he died and no one else had co-signed for any of his loans, only his estate would be responsible to pay any outstanding debts and only after the burial expenses are paid. I am not a lawyer and I would suggest you check with one, but I believe, no one may be obligated to pay any of them.
My son died with a small credit card balance. The bank called to see if the balance would be paid. Since there was no money left in his estate after the burial expenses (essentially he had no estate and I paid all of the burial expenses), there was no money to pay the outstanding balance. They asked if I would pay. I asked if I was obligated to pay. They said 'no' since I wasn't on the account. Then I said, 'I wasn't going to pay'.
Even though you may feel morally obligated to pay the bills, check to see if you are legally obligated to pay them before you do so.