I can't imagine that the car would be able to pull fuel and run after creating so much vacuum that the tank bent.
Very typical on Small engines (lawn mowers) the engines stall after about 10 minutes if the Vent is clogged.

 

That will teach me to answer a question when I haven't slept for almost 18 hrs. Original tanks were vented, replacements one were not. When replacement was made, it was done with a non vented tank and aftermarket gas cap.