The 'hot side' is always outside the box, I can't think of way for a fridge to run in reverse but I certainly haven't spent an enormous amount of time poking around domestic fridges
Way more fundamentally though, if the interior gets very cold then the thermostat just won't kick in anyway. The fridge won't try and run 'cause the inside is already cold. At which point it just becomes an overblown cupboard?

