Outstanding debts at the time of death generally pass to the deceased person's estate. State laws may vary on how a mortgage is handled in this case, as matters get complex when deciding if other liquid assets in the estate (e.g. a savings account) must be used to repay the mortgage first, or if the mortgage itself can be inherited as-is, whereupon the inheritor will assume its debt.

This discussion on WikiAnswers presents one such scenario: http://wiki.answers.com/Q/Is_a_mortgage_considered_part_of_the_debt_of_an_estate_to_be_paid_by_the_estate

And this article on MyStateWill.com goes into much more detail on the subject: http://www.mystatewill.com/info_files/mortgage_payment.htm