It may be of unlimited value. However, if you are behind on your mortgage payments and are subject to foreclosure, understand that a Chapter 7 Bankruptcy will only delay foreclosure. If you are current on your mortgage payments, you will have to make your payments before, during, and after the bankruptcy. Bankruptcy won't eliminate most liens on your home - your home is security for the loan. Most lien holders have a right to foreclose if the lien isn't paid off within a specified time.
Most lenders are willing to negotiate.
Recognize, they really do not want the home. What the lender agrees to will depend upon your credit history, the reason for your missed payments and your financial prospects. For example, you miss a few house payments because you had a car accident and couldn't work for two months. It looks like you will get back to work soon. In this case the mortgage company will most likely make a deal with you rather than move for foreclosure.