I sympathised when I read about the snapped tail of your old cat. Years ago, my cat went missing for several days. I called and called her, but would sadly go inside when she didn't come. I thought she was dead. Then one night I went through the same routine, but realized it was rubbish collection the next day, and went outside again. And there, sitting quietly, was my cat. She was very thin, and her tail was dragging along the ground. The vet said he thought she had been hit by a car, that her pelvis was broken but would heal OK, but that I ought to have her tail removed when she had recovered sufficiently.
Thing was, she had a habit (don't they all?), when I was reading the paper, of stalking over the page I was reading and then sitting on the exact paragraph, all innocent. And I had a habit of running my hand along the spine while she walked past, and then gently tugging on the tail. I completely forgot about the broken tail, until I heard (and felt) it go click. From then on, she had movement in it, albeit kinky and not terribly elegant, but no feeling obviously, as I realized later when both of us looked around for the source of the burning smell one night, and found it was the tip of her tail, in the heater!
That old girl lived to 20 years old. For the last three or four of those years, she had medication for an overactive thyroid. She was a darling old cat, and in the end she was a querulous old lady, demanding food and a hot water bottle, and sleeping her days and nights away. I miss her still.
With your old girl, I'd be inclined to get a really good flea comb, and do some one on one bonding with her, by grooming her coat. She'll feel better, you'll get some fleas and eggs off her, and you'll have given her a real boost.
Good luck!