In New York, you can use the Homestead Exemption to protect equity in a home.
In order to use the homestead exemption, you must own the home AND live in it as your residence.
The homestead exemption is $50,000 per person and a husband and wife who are both on title can double the exemption to $100,000.
If you are talking about a house that you do not live in, the trustee can take your interest and sell it for the benefit of creditors, even if your parents are living in it.
You would probably benefit from the advice of legal counsel.
For more information about various aspects of filing for bankruptcy, please see my Bankruptcy Blog which contains several hundred articles about filing for bankruptcy on Long Island.