I was in a similar situation some years ago, I took the cat in, took it to the vets and took ownership of it. Some months later I went to the doctors and the receptionist asked me how the cat was, it turned out it was her cat, and she knew I had taken it in. She didnt mind, as she said it had run off when she had a puppy, strange though, as I also had a dog! We moved house shortly afterwards and took it with us. So my advice, take it in and look after it if you feel like you want to, as if it looks that bad, the owners obviously dont care anyway.