When a home sis sold for less money than will pay off the loan(s) and the closing costs, it is called a "short sale". In order to conduct a short sale the lender(s) who "owns" the loan(s) has to be convinced that it is the right thing to do (as opposed to foreclose).
Part of that process is presenting the case, referred to as "hardship". Death, divorce, medical issues are often the primary reasons for a sale. Depending upon the amount of "short" in the sale, the lender may say yes or no. Because this is a divorce I would think that both attorneys should factor this into the settlement. I heard about one case in which the wife was allowed to keep the house in return for giving up her share of her husband's 401K.
Good luck. You are going to need a Realtor experienced in short sales if you need to sell.