You probably have to be willing to follow through for this to work, but my husband's father was driving his car and heard this horrible sound. When he stopped, he found that his niece's cat (she was staying with them) had crawled up into the engine compartment to get warm and got mangled by the running engine. He took the cat to the vet and told the vet, "This is a $100 cat. I'd like to get him fixed, but I refuse to spend more than $100. If you can fix him for $100, do that. If not, then put him to sleep." The cat was treated from its severe injuries for exactly $100. He's sure it would normally have been several hundred dollars, but people go into veterinarian medicine to help animals, not to put them down.

Sorry about you cat having health problems. It is painful to pay huge vet bills, but we get attached to our pets.