I never knew that cats did that sort of thing. I sympathize with the neighbors though. It is very sad that the cat may need to be put to sleep, but I have experienced living with a neighbor who had a pet that made you afraid to go outside and it is deeply unpleasant.
The people next door to me should never have owned a dog, and they abused the string of them that they did have that all mysteriously died after a few years of kids shooting firecrackers, etc. Anyway, they let their 4 year old walk the lab-sized dog, and one day I was walking home from babysitting and the dog dragged the kid across the street and leapt at my throat. I caught it by the collar and held it up in the air which probably hurt it, but the da** thing was trying to kill me, so. Animal control was called several times, esp once after it killed someone else's dog. They were forced to put a couple to sleep. And just kept getting new ones.
I couldn't even go in my backyard.
So, perhaps it would be best for everyone if the cat were put to sleep and the owner never allowed to own a cat again. It seems insane that a cat could do so much damage that a few people had to go to the ER! Obviously something is very very wrong there.