Your best option is to find another apartment. Basement apartments are usually illegal (I have never seen a legal basement apartment) and can be dangerous if there's a fire or any other problem. With respect to paying the rent, the owner is still the owner of the property and if you have a legal obligation to pay rent, the owner can still begin eviction proceedings against you for unpaid rent. A short sale process is merely a sale where the owner owes more on the property than he/she can sell it for. Good luck. If you want further information, you should speak to an attorney.
Century 21 Princeton Properties