This is important enough that you should consult an attorney specializing in franchisee-side transactions. You're probably already aware that your franchise agreement may provide for "liquidated damages" (you'd probably consider them penalties) for early termination. I would be surprised if you were able to open a franchise and not have a personal guarantee in your name on any of the documents. That said, if you did manage to avoid a personal guarantee of the franchise contract, it might be difficult for them to attempt to make any claims against you personally, but not impossible.
As far as your landlord goes, it depends on who your lease names as the leasing party, and whether you personally guaranteed the lease.
For the exposure you're facing, it's probably worth it to spend a few hundred dollars to have an attorney review your franchise documents.
Do not do anything without talking to a lawyer. You probably wont have to spend a lot on legal fees but considering what you spent on a franchise do yourself a favor and spend a little more. A number of franchise owners go under. What does your agreement say about selling the business? Have you spoken to the franchise developer? What are they saying about your financial issues? Rent can only be part of bankruptcy if it is in the corp. name that is filing for bankruptcy.Most of the time once you incorporate you can not be held personally liable but there are exceptions. See what I mean? Talk to a lawyer.