We had a similar incident with one of our cats only we know exactly how it happened. He ran out the door one morning while were were leaving for school without us noticing, went and laid under the car right under the engine. Dad started up the car and he must've done the whole standing straight up with his tail raised bit because he got it caught in the fan and next think know we see a gray blur running up the porch. I got out've the car and let him inside, we hadn't noticed the tail yet because he wasn't acting hurt and he didn't yowl. That night when I was feeding him I noticed the bone sticking out of his tail. It'd already scabbed over and the bone was drying out and it was only the very last two joints so we just left it and it fell off.
We have a black and white cat exactly like that. 30 pound male, he's big but also fat, we call him 'Blob' even though he's technically named Farrell (was a stray, play on words). You can pick him up and turn him over on his back and he'll just stretch out like he's dead and let you carry him around like that, very passive cat. He is scared of strangers though, somebody comes into the house he doesn't know and he hides for the duration of their stay.