Would a car stalling happen if you had a leak of some sort?

Yes, if you have a severly blown head gasket, it is letting coolant into the cylinders. If too much coolant gets in, it will cause stalling, usually only at idle speeds. i would suggest getting a compression test done and checking the head gasket, and most likely, you will need it replaced, if you cant do it yourself, it will be close to $400 for pats and labor, $350 is prabably labor. Labor sucks!