RE: Getting to Know the Local... Cats
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.
I had suspected it was something related to cars, but in my knowledge (none), I couldn't figure out how a tail burned off + limp could happen. Given I'm in a country that casually and happily tortures dogs by throwing them, alive and well, into a burning stove as their feet melt off (because the adrenaline makes them taste better obviously), I also suspected human maliciousness.
But yeah I'm sorry to hear the pain of your cat but it's great it's getting along fine. I hope in the end someone did capture this one and it's living happily but... who knows.