Heirs inherit both liabilities and assets. The estate is responsible for liabilities, and the answer to whether that includes the mortgage is not within my scope. But, I believe that is definitely worth pursuing.
If the estate does not have liquid funds, or they simply decline to pay, your lender will enforce it's rights to collect in any way it can. If you are able, it might makes sense to pay the full mortgage and protect your interests in the property, and your credit. Collect what is owed to you later, but protect your credit now.
Hope that helps.