In most cases, you are not responsible for paying off your parent's debt. Nerd Wallet explains that there are only a few cases in which you are responsible for paying off their debt. If you co-signed a loan with your parent, if you are a widow/widower in a community property state (Alaska, Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington and Wisconsin), or if you are the executor of the will . Also, if you and your parent had a joint credit card, you will be responsible to pay, even if you didn't make the charges . In all other cases, you are most likely not responsible.
This means that when creditors call, if you don't fall in this category, you can simply hang up. Creditors will try and make you feel guilty and get money out of you, but it is not your responsibility. If you become tired of having them call, you can write a letter and ask to be taken off the calling list or contact the Federal Trade Commission (FTC) .
If you do fall into that category, it doesn't mean you have to pay it out of pocket. Usually, the estate will be expected to pay. This means that all of your parent's remaining money and property will be sold in order to break even with creditors. If the estate runs out, then essentially creditors are out of luck and your parent's debt dies with them. Also, keep in mind that before any heirs of the will get their money, the creditors must all get their money. So once the estate runs out, the creditors won't be the only ones not seeing a penny .
If you inherited a house with mortgage, check with an estate lawyer to see exactly what you need to do. Since these cases are complex, there is no blanket statement to cover every incident. Remain open to idea of having to sell your parent's house if the mortgage is higher than the value of the house .
Remember that individual situations vary, so contact a professional for more information on your specific situation.
 When my parents die, will I inherit their debt?
 Am I liable for the debts of a deceased parent or spouse? FreeAdvice Legal
 Can you inherit your dead parent's debts? CNN Money