North Carolina Bankruptcy Attorney Susan Robicseck has a very good post on her blog about why you are not liable for a deceased persons debt.  Kentucky law is very similar here to North Carolina law in that the deceased’s assets are liable for their debts:
The smartest thing to do is get legal advice very quickly after someone passes away to make sure whether or not you are legally required to pay a debt the deceased person incurred.  If not, it may not be necessary to file bankruptcy on the debt and you could avoid bankruptcy.