When a person dies, their assets are pooled into what is known as an estate. The estate is responsible for paying the debts of the deceased. If there aren't enough assets in the estate to pay the debts, some creditors will hire a collection agency to pester the deceased's relatives for payment. These collectors will often imply that you, as a relative of the deceased, have a legal obligation to pay for the deceased's debts. This is almost always incorrect. You almost never have any obligation to pay for the debts of a deceased relative, even if you are named the representative of the estate. The only time you may have an obligation to pay for a deceased relative's debt is if it was a joint debt that you agreed to pay for, such as a joint bank account or if you co-signed a loan with the deceased.
No matter what the supposedly sympathetic bill collector tells you, it is rare for a person to be legally obligated to pay for a deceased relative's debt. You should consult with a lawyer before agreeing to pay anything.