At the household level, such "double triggers" may induce defaults because of cash flow constraints or because continuing to make payments on a mortgage whose balance significantly exceeds the value of the house is more difficult to justify when the family budget is strained.
See Shane Sherlund (forthcoming), "The Past, Present, and Future of Subprime Mortgages", Finance and Economics Discussion Series (Washington: Board of Governors of the Federal Reserve System); Kristopher Gerardi, Christopher L. Foote, and Paul S. Willen (2008), "Negative Equity and Foreclosure: Theory and Evidence", Public Policy Discussion Papers 08-3 (Boston: Federal Reserve Bank of Boston,  BIS Review 152/2008  5  If one accepts the view that principal write-downs may be needed in cases of badly underwater mortgages, then strengthening the H4H program is a promising strategy, as I have noted.