Stuff like this happens all the time. It happened to me last year. In my case, the deal was approved over the weekend and I kept calling to make sure things were ok. On Wednesday of the following week, I was told that the financing fell through. I politely brought them their truck back and picked up my trade-in. Thankfully it was still there!!
Most dealers now send the customer off with their new vehicles after having them sign a fuzzy document that states that the deal is contigent upon "final bank approval." If you can't get financing through your bank or credit union before you go to the dealership, I suggest not taking possession of the vehicle until the bank has given it's final ok and/or you get your payment book. Otherwise, you're stuck with the car. And a high interest rate or payment, with practically no recourse.
Starting Scores: 12/14/14 FICO EQ: 579 EXP: 586 TU: 591
Current Scores: 12/29/15 FICO EQ: 643 EXP: 667 TU: 670
Goal: 750