I've definitely seen that tail effect before. That's what happens when a cat has crawled up into the engine compartment of a car or truck for warmth and rest when it is cool out and the engine is still warm and their tail has become entangled with one of the belts which goes into action when the engine is started. It'll strip the skin off the outside of the cat tail but not usually be fatal, allowing them to run off. If they survive the ensuing infection, the withered bit can often be gnawed off leaving only a little fur-less stump and they can survive for many years.

That is exactly what happened to one of my cats when I was a kid and it continued to run about and father offspring for quite a while.

It's the potential infection that's a problem.