The seller would have some rights to negotiate. Of course, the borrower would want to recoup some of his/her loss. They can get authorization from their bank to accept an offer for less than the principal balance (what they owe), but not all lenders will do this.
In the event that they owe more than the property is worth, they can *sometimes* (depending how deep they are) sell the house for a lower price and eat the rest to try (take out a loan for the remainder) and save their credit.
In either circumstance, the benefit for the seller would be that they could salvage some sort of dignity out of their credit…however much is left. Having delinquent payments is better than having a foreclosure.
You would be suprised, though…sometimes a loan is delinquent because the borrower has passed on. In these circumstances the property sometimes goes to a trust or probate…though there are times that you would be able to negotiate a price with the next-of-kin who would want to just get the property off his/her back.