Legal Question in Credit and Debt Law in Massachusetts

If a judgment is entered against you in the car case, the judgment holder could attempt to get a lien on your property (assuming you mean real estate). If it's personal property (jewelry, collectibles, etc...) it might be harder for them to prove you're an owner. If it's a bank account they can try and attach it. The most important thing for you is to try and prevent them from getting a judgment against you. You may have a defense for why you were in breach of the lease.

When you say "property" I assume you mean real estate. There are methods available that could allow the leasing company to take your "share" of the property, things like partitioning, levy/sell, etc. As a practical matter, if there is little or no equity in the home, it won't make sense for them to do it because they won't end up with any money after the mortgages are paid off first and foremost. Depending on the amount that they are seeking, it may be possible to work out an agreement for repayment with them. Of course, if you feel that you did not violate any agreement, then the lawsuit must be defended so that they don't even have an opportunity to come after the home. A bankruptcy filing could possibly erase this and other debts, if you qualify.