One assumes that most debtors would not consent to a deed in lieu in these circumstances. However, some debtors might be so psychologically overcome by their financial difficulties that they are willing to throw in even a very valuable towel.
If a debtor's "paper equity" in real property would be substantially eaten up - - by a depressed bid and foreclosure costs in a foreclosure sale or by commissions and closing costs in a voluntary sale - - a deed in lieu might be for reasonably equivalent value even if the value of the property is somewhat more than the amount of the debt being extinguish