In real estate an assumed mortgage occurs when a the buyer of a real property is transferred all the obligations of the seller's mortgage.
The buyer assumes all the obligations under the mortgage, just as if the loan had been made to the buyer. The major driving force behind assumptions is the lower interest rate on the assumed mortgage relative to current market rates. This method is frequently used when the buyer can not get a better interest rate than the seller currently has.
When a homeowner sells their house they will ask for the equity they have obtained (Sale Price - Amount Owed). Under an assumed mortgage, they will also transfer any obligations to a bank, on to the buyer. In the event of a default, the bank (as a creditor beneficiary) has the right to assert their interests against both contracting parties.