When is it too late to work out a deed-in-lieu of foreclosur

My father is a builder trying to overcome the unsteady market. Over the last year he has had trouble selling a few of the houses he built or bought when things weren't so bad in our state. He managed to sell all of the properties except one. He and my mother paid the mortgage on the property for as long as they could but claim to have had a payment refused by their lender when the lender asked them to pay property taxes that were already paid. To make a long story short the home is in foreclosure and I am concerned about a deficiency judgment. Today my mother told me the sale of the home is scheduled for later this month. Is it too late for a deed-in-lieu of foreclosure?