This is a cat D. and I called Lap Kitty. Every time we saw her she would determinedly climb into our laps if we crouched down even a little bit. She was declawed but didn't seem to have her own home anymore. One evening we saw a woman sitting on the sidewalk with Lap Kitty in her lap. She said she'd been keeping an eye on her recently and if her own cat wasn't dying she'd bring Lap Kitty home right away.
We haven't seen Lap Kitty in a while, so maybe that woman adopted her.