We had a cat that moved in like that. My grandfather died, and I stayed with my grandmother for a month to help out. I came home and this scrawny black cat is in the back yard under my rose bush. I asked my husband about it, and he said that if we didn't feed it, the cat would leave. I asked how long he had been out there, and he said, "since you left." I let him know that his theory wasn't working and went out to see the cat. He was starving, declawed, and had a mass of sores all over his face, from infected bug bites.
Since we weren't (supposedly) keeping him, I never called him anything than the "Other Cat" (as opposed to my cat inside.) Needless to say, I cleared up his face and even got fur to grow again, although if you were close to him you could still see the scars. He wound up named Other, and he was a wonderful, loving cat. He used to sleep in the back yard, and every once in awhile I would get a knock on the front door about the dead cat in the back yard. He would sleep on his back with his limbs akimbo, his mouth open with tongue hanging out, and eyes rolled up in the back of his head. Twice I had to grab and wake him before the ladies knocking would believe he was alive.
I miss him, too. He'd drool like you wouldn't believe, too.