This reminds me of one of our families cats, Thunder.
We were tearing up the front yard (It was mostly clay, and weeds were everywhere so we had to renovate), and he came and stuck around while we worked. We thought he was adorable, but belonged to someone else so we didn't take him inside that quickly. He kept his distance from us, and we were heading inside while he was eating.
Apparently he fell in love with us because he started to camp outside our front door. For a solid week he didn't move from our porch at all while we fed him. During that time, we took pictures of him and posted them on our cities facebook page (trying to find the owner) because we thought there was NO way a stray cat could be as well behaved and nice as he was. No success, so we started to go out to pet him.
When we did, we found out that he had a variety of health problems. He was sneezing blood, he had a mite infection in each ear, and (though we noticed this earlier), he was skinny as hell.
Naturally, once we noticed this we took him to the vet as soon as we could (the next morning). He was cleaned up and vaccinated (and the veterinarian was kind enough to offer us a discount for a neuter), and we brought him home.
He was a bit bo-legged from losing his balls, but he recovered quickly. He let us pet him, but only on his back. Cheeks, chin, and belly were all off limits. I said before he was well behaved, but he was definitely not "domesticated" at the time.
He eventually lightened up to the point where we could pet him wherever we wanted. And essentially, he was also the perfect cat at that point. He seemed to never shed, or claw at the carpet/furniture. He never got fat, and always ate meals in decent portions. And his fur was like silk, seriously.
Anyway, Thunder passed away a week ago. I don't have any pictures on my computer, but if you all want I can follow up to this comment with some.
And also, sorry for his life story. Kinda felt like I had to type it all. He will be missed.