Special relativity implies the possibility of some apparently paradoxical situations, which can ususally be made sense of if one applies the theory rigorously. One of these is the car-garage paradox: a car speeds towards a garage which, at rest, is slightly shorter than the car. From the reference frame of the garage, the car appears shorter, so that it will fit into the garage (if the speed is high enough, which we assume it is). From the reference frame of the car, the garage appears shorter, so that the car will not fit. I have seen some very nice solutions, like this one, where the garage has a front door and a back door and the caveat is that their opening and closing times depend on the reference frame, so that in the end the car gets through in both cases, although in one case it is longer than the garage.
But what happens if there is only a front door? Of course the car will eventually crash, so that there are some non-inertial computations involved, if one wants to do things rigorously. But in any case, if the garage door closes immediately (let it be almost as fast as light and very small) after the rear of the car has passed it, then in the garage's frame the door will close and then the car will crash, whereas in the car's frame the door will not be able to close, and since after the car crashes (decelerates to $0$) it is still longer than the garage (neglect shortening due to the accident), the door will not close at all, ever. But this is impossible, since the fact that the door is closed or open for all future times should not depend on the reference frame.
Is there a way to make sense of this applying the theory of special relativity and without waving hands and just saying "this situation is not physically possible"? I know it isn't, but one can certainly modify it appropriately so that it is (e.g. transforming the car into a particle and the door into a sensor,...).