Very good answers below, particularly the one that suggests talking with a CPA.
The truth is that you have an obligation. If you want to sell your home for less than your owe, you still owe the money. A lender may allow you to sell for less than you owe, however you will receive a 1099 for the difference, which will include closing costs.
California has special laws regarding this, so talking with a CPA is important. And if you need legal advice, talk with an attorney.