In most states, lenders have recourse. So if you stop paying your mortgage, the bank will foreclose on your home and then come after your other assets to make up the difference in what you owe vs. what the home is currently worth.
(not legal advice, educational purposes only)
Apparently, there are only 10 non-recourse states as of 2009: Alaska, Arizona, California, Hawaii, Minnesota, Montana, North Dakota, Oklahoma, Oregon, Washington, and Nevada. The tricky thing is that only the initial mortgage is non-recourse. A refinanced mortgage becomes recourse, but interestingly, they don't seem to be required to disclose that in the disclosures.
Washington isn't really non-recourse, lenders have the option of recourse or non when pursuing foreclosure, non-recourse is significantly faster and is predominantly chosen; but if it was known you had assets, they might choose to go recourse.