The answer depends on who would be taking over the mortgage payments. If the person taking over the payments is a relative of the deceased person, then yes, payments can be taken over. But generally speaking, a transfer of the property to a non-relative triggers something in the mortgage called a “due-on-sale” clause. The due-on-sale clause means that the mortgage company is entitled to payment in full if the property is transferred to someone other than the borrower. Due-on-sale clauses apply to most transfers, whether there is an actual sale or not.
There is a federal law that says a due-on-sale clause cannot be used by a bank to demand full payment if the transfer is to a relative upon the death of the borrower, to a joint owner of the property upon the death of the borrower, or to the borrower’s spouse or children. There are some other exceptions as well, but none apply in this circumstance.
Alternatively, the person wanting to take on the mortgage could agree to purchase the property, obtaining a new purchase loan to pay off the existing mortgage, or possibly apply for a refinance. In some rare circumstances, a bank may also agree to an assumption of the loan by the new owner/borrower.