Answer:
Improve
If the estate has no assets, then technically no one is responsible. If the hospital (or whoever the money is owed to) decides to sue, they'd be suing the estate, which has no money, which is just pointless. The family can pay for the medical bills, but I don't think it's necessary. If you are the Executor of an estate, you should probably meet with an attorney anyway.
This is the reason to create an estate. It provides an opportunity to gather all the debts, pay off whatever the estate can pay off, and have the rest officially closed off so that the debtors don't keep bugging the family.