This is a fun issue to deal with. I know this not because I've ever sold cars (I haven't and never will!), but because something similar has happened to me in the past. The deal to buy a car is usually written pending finance. They sell you your contract on the contingency that your loan is accepted by a specific bank. If not, then they do what they can for you. In some cases they sell the car by assuming the bank will accept it when in fact they haven't looked closely enough at your credit report. Weeks or months later, after they tell you that you haven't been accepted, you have the option to return the car or accept their new financing deal. When you tell them that you want your old car back, 99% of the time they will tell you that it has already been sold to another customer (I've been told by car salesmen that this is done to keep you from cancelling the deal, even if you car hasn't been sold. Often times it is sitting on another lot waiting to be sold). This leaves you in a position where you have to buy the car you were originally trying to buy under their new terms.
My advice, tell them no deal and ask for your old car back. When that doesn't work, tell them that you'll be dropping off the new car along with the keys, and you expect to be reimbursed for the car they sold before your financing was approved. At that point the dealership will sometimes finance you themselves under the original terms in order to avoid potential legal problems.
Depending on how the original contract is written though, they might have you over a barrel. I generally like Mitsubishi's, but coincidentally, it was a Mits dealership that I had my problem with. Coincidence?
