can someone suing you for assault claim your house you live in ?

I someone gets a judgment against you, they can place a lien on your house for the amount of the judgment.  If you don't pay the judgment, the judgment creditor can foreclose on that lien to collect on the judgment.  In some states, a person's residence is exempt from collection efforts, but in New York I believe it is only exempt up to $10,000 in equity, meaning that if your house is sold for more than $10,000 above what is owed on it (to mortgagees), the excess can be seized by the judgment creditor to help pay the judgment.