So far, Washington has put its political capital into trying to refinance salvageable homes for unsalvageable homeowners, when a relevant policy would consist of judiciously buying unsalvageable houses and demolishing them. Fannie and Freddie's strength is housing market software: They could be put to work devising a least-cost, maximum-bang strategy for demolishing unoccupied homes to preserve as much value as possible for the homeowners and mortgage creditors who remain.
That sounds like advice from the Depression, when concern with excess supply led the government to slaughter pigs and burn grain.
I don't think it's a good idea to destroy houses. If we had more legal immigration and less illegal immigration, then we would have more home buyers and fewer excess construction workers. Seriously, I think that with two or three years of reduced home building, the excess supply will be absorbed.