There is an estate! If you haven't opened one, you should. The estate is responsible for the debts. Consult an attorney for the area that you live in for specifics.
It is not the parents, but the estate that is responsible for any remaining debts. That will include medical bills. If there is not enough in the estate to cover them, someone will not get paid.
Typically they shouldn't be. The debts of the deceased are the responsibility of the estate. Anyone that was also a co-signer on any of the agreements might also be responsible. Consult a probate...
Generally, the dedecent's estate is responsible for the debts of the decedent. If there are not enough assets to pay the debts the estate is declared insolvent.