I was sort of fostered by a cat once. I was far from home and feeling a bit apprehensive. I had a tiny apartment on the first floor and I left my window open. Imagine my surprise when I woke up with a cat on my bed.
He spent every night with me for a year. I never gave him a litter tray or fed him except scraps of what I was eating - but he came every evening and sat on my lap and slept on my bed.
I assume he had another home somewhere in the block and I assume he went out of their window to come in mine (there was a sort of stone parapet about 6" wide running round the whole city block).
I never gave him a name because I didn't feel he was mine. So I called him No-Name.
And then one day, the day before I was due to leave, he didn't come back.
It was like he knew I didn't need him any more.
He looked a bit like Davis - I don't think he was a particular breed but he was large and very, very hairy!
Edited - oops, I meant 2nd floor!