There is a stray cat in our neighborhood that actually looks almost exactly like one of my cats (which always makes me do a double-take). I've tried to approach it before, but it always runs away. I have thought about calling the shelter, but I wonder if it would just be put to sleep if it has a fear of people. Is there anything I can do for the cat?

I think it likes my neighborhood because I have a bird feeder (and several large squirrels who like to come dine too), and sometimes I see it stalking them. I don't want them to end up lunch though, either.