Reuven Brenner for Forbes thinks a lottery might be the solution to the foreclosure and shadow inventory mess. He got the idea from Thomas Jefferson:
Shortly before Thomas Jefferson died, he tried to pay debts that amounted to $80,000 by disposing of land he owned through the use of a lottery, a well-established method at the time. He explained the rationale for such financing: "An article of property, insusceptible of division at all, or not without great diminution of its worth, is sometimes of so large value that no purchaser can be found ... The lottery is here a salutary instrument for disposing of it, where men run small risks for a chance of obtaining a high prize."
Go here to read how Brenner thinks it could be made to work.
