Cassie (originally Cassiopeia) somehow hurt herself a few weeks ago, possibly from slipping and falling. I knew something was wrong when I heard a loud "thump" in the other room. I hobbled in to look, and she ran from me. She was holding her tail at an odd angle, and not moving it (she's quite the tail talker), so I knew something was wrong.
I transported her to her Dr. Doolittle of a vet the next day. She had, as I remember, bruised the last vertebrae before her tail starts, and sprained her tail. I did not know that the nerve bundle at the base of a cat's spine helps them defecate. She was quite swollen at the base of her tail.
After repeated trips to the vet, the swelling has gone down, but she still has a big lump on the side of her tail. I've tried to catch her in the litter box just to make sure everything's working as it should, but she's always been very elusive about eliminating if I'm near.
I'm posting this mostly because I didn't know about all the functions of a cat's tail. I knew they were important for balance, and they use them to communicate, but I didn't realize there's more to it.
So, if your cat ever falls and then doesn't move their tail much, take them to the vet as soon as you can. The sooner there's a veterinary intervention, the better chance they have of good recovery.