Yes — and inheriting a house does not mean you automatically inherit the debt personally in most cases. However, the mortgage, property taxes, and any liens recorded against the property stay with the property itself. If you want to keep the house, you will need to take over the mortgage payments or refinance into your own name. If the estate cannot cover the debts attached to the property, the home may need to be sold to pay them off.
Heirs are generally not personally liable for the deceased's mortgage debt — that debt is secured by the property, not by the person. But if the estate has more debt than assets, the heirs may end up receiving little or nothing once the property has been sold and the obligations paid off. Understanding exactly what is owed on the property before making any decisions is always the right first step.