In my state we have a few organizations, they feed the strays and get them spayed and neutered, and shots, then set them back. This helps with the population of cats as well as not taking their freedom. In some cases, they are given to foster care, and then adopted out.

My experience has been, I have fed the cats, then slowly gained their trust, and then they've become my loyal pets.

What I would do, is call around or search online for websites for organizations to help cats, or like a few posts have said, search for a no kill animal shelter.

Annie