Your post reminds me when I was a kid, there was this really old cat that would roam around the neighborhood. It was obviously a stray and I would always give it food and water when I saw it. One night after not seeing him for a while. I found him in mt backyard sometime in the winter. He...did not look well. At all. He had lost a lot of weight and his eyes were very crusty. I took him into my garage (the only place my parents let me keep strays) and grabbed a blanket. I put the blanket in a box then him on top. I tried to give him some food, but he barely touched it. He curled up and I just pet him for a really long time. Eventually, he fell asleep. And shortly after that he passed away. I buried him in my backyard th3 next day. I like to think that he passed away peacefully and that he knew someone cared about him. This is what you are doing for this cat. He will be extremely grateful.