Swapping Debt for Equity

Under Chapter 11 bankruptcy frequently creditors agree to reduce the principal in exchange for equity in the newly created company. A couple of years ago I had this idea - why not apply the same principle to homeowners. The banks get (future) equity in the house and the borrowers get principal reductions and the housing market might even recover. Sounds like a win-win-win proposition. Clearly this blogger agrees:

http://finance.fortune.cnn.com/2011/09/01/a-mortgage-fix-for-lenders-and-homeowners-shared-equity/

But the more I thought about it, the more problems I find with the idea. Why would any borrower stick around once there's any equity in the house? As soon as they can sell the house and pay off their mortgage they would, borrower has a clear slate, bank gets nothing for their equity stake. Nin-Hai proposes that there much be a certain dollar amount of equity in the house before the person is allowed to sell. But it seems like those types of clauses would be a nightmare to enforce, plus it locks the person into their house for even longer. Also what bank wants to take on more house price risk? So I think its an interesting idea but ultimately impractical.