If a borrower defaults on the loan and the seller remains liable under the terms of the promissory note, what type of mortgage is this known as?

The situation described refers to a "subject to mortgage." In this arrangement, the buyer takes over the mortgage payments without formally assuming the loan, which means that the original seller remains responsible for the mortgage, even if the borrower defaults.

In a subject to mortgage, the buyer acquires the property along with the existing mortgage, but the mortgage remains in the seller’s name. Therefore, if the borrower fails to make payments, the lender can pursue the seller for the debt because they are still liable under the promissory note. This setup can be beneficial for buyers who may not qualify for a new loan or wish to avoid the costs and complexities associated with obtaining a new mortgage.

This contrasts with other types of mortgages listed in the question. A due on sale mortgage requires the loan to be paid off upon sale of the property, placing more responsibility on the buyer to obtain new financing. A conventional mortgage typically does not have these implications regarding the seller’s continued liability. An assumable mortgage allows the buyer to assume the loan with the lender's approval, which may release the seller from liability depending on the agreement.