I found a cat that I believed to be lost because it had a collar on with a phone number and an address, and because it seemed very friendly and very much like an indoor cat. Yet, when I took the cat back home to its owner she did nothing but shrug and say "just leave her outside, she's fine". Why would you put a tag on a cat if you don't want anyone to return it when they find it? Do you think she's hoping the cat runs away or gets killed? Should I find it a new home?
There's got to be a pet owner like that in every neighborhood; a person who leads you to believe they give a crap about animals when they really don't. Considering the cat has a tag on I do not suggest you take it and find it a new home. That would be stealing. However, there's nothing wrong with you keeping an eye out for the cat and checking on it once in a while. If, at any time, you believe the cat doesn't look well you would have grounds to call Animal Control to report the owner for neglect. Fingers crossed the cat just really enjoys being outside during the day and then goes home at night for food and tummy rubs.
Keep me posted,