There is a 9 month history to this tale but I will extremely brief it.
9 months ago a very neglected looking cat appeared in my garden: I'm talking underweight, discharge from her eyes, some cuts on her face and lots of fur missing off the backs of her legs.
Because of how awful she looked me and my husband fed her thinking she to be a stray. She continued to visit so a few days later I took her to the vet for a general check over and to see if she had a micro-chip but she didn't. She is a very gorgeous tabby, about 3 years old. After about a month of her still coming to ours every day it came out that she wasn't a stray at all but had owners who lived on the street next to ours. It upset me actually as I realised that the poor state she was in when she first arrived at ours was just the state her owners were happy for her to be in.
Skip to now - the cat has never stopped coming to our house and spends a lot of time here. She also sleeps here every night. Her owners have said they throw her out every night regardless of how bad the winter weather is 
Her owners know how much time their cat spends here, they know which house I live at and they have my mobile number but they have never contacted me to ask how their cat is - sometimes she is here nearly all day for weeks on end and I don't hear anything from them. I have made contact with them 2 or 3 times to let them know that their cat is here and that she is ok (just in case they were worried about not having seen her for a while) but the responses I get back indicate they don't really care.
This cat's health has deteriorated over the last few weeks - if it was one of my cats I'd have had her down the Vets a long time ago. It's really worrying me. I know she has been back to her own home a few times over the last week so they must see what state she is in but I doubt they care enough to do anything about it.
It upsets me to see the cat in this way and I want to take her to the Vet but at the same time, treatment is not cheap and why should I when it isn't my cat? AIBU to just take her and then knock on the owners door and hand them the bill?