I tend to keep my animals until they are old and wonky .......I do feel for you, and the cat,too, as this sounds awful. I find the older cats struggle with eating sometimes, and I try to mince their food, and some of them can eat it much better. Funny enough they seem able to cope better with biscuits than the tinned meat
I look after my neighbours cat while they are away. It must be nearly 20, and unfortunately recently has developed all sorts of ailments. Thyroid gland problem, liver problem, etc. etc. Went as thin as a rake, and when they took Poppy to the vet, I honestly thought that was it. But, back she came, and after a course of tablets, she has perked up, and looks lots better. Am looking after her for a fortnight now, so hope she does not die on me. There other cat who was old, took a bad turn and I had to take her and have her pts while they were away!!