When someone dies that you owe money too then usually the persons family members or other estate will take over and contact you for the money you owe to them.
If the money you owe is a small amount $100.00 or less then they likely won't chase your for the money but if you owe a larger debt to the deceased person then the persons family or estate will contact you to collect.
If you're buying something such as a home through a contract for deed then once again either the estate or family should get into contact with you letting you know about the deceased person and how and where to send the payments to pay off the debt.
Then they will take over the contract etc.