This should be similar to a guaranteed student loan. The idea would be to allow consumers to take out a loan for the difference between the amount owed and the homes value. This would allow the owner to sell the home at market value, or refinance to take advantage of the current rates, without having to default on the loan. They would continue to pay the guaranteed loan after they'd moved to their new home.
This should stimulate home sales and facilitate people moving for better jobs, as well as greatly reduce the exposure to loss that banks are currently facing.
This loan would have similar rules and governance, as well as low interest rates, that student loans have.