Generally speaking, Frye said, you're not obligated to pay the bills a decendant leaves behind. But you won't be able to inherit any part of the estate until creditors are made whole.
The estate's assets are inventoried under probate, liquidated as necessary and used to pay off any tax liabilities, secured debt (mortgages and car loans) and unsecured debt (credit cards and personal loans). Whatever property remains is then distributed as the will directs.
If assets are insufficient to cover liabilities, the lender typically takes the loss.