Thank you all for your prayers and replies.

Please see my NOTE in my update. Kitty is NOT declawed.

A bit more news about this situation. I went earlier tonight to tell my neighbour about what the vet said about Kitty, (that's what I call the cat) and while I was talking to her, the sister of the woman who owns Kitty came downstairs and walked right by us.
Apparently the sister goes and feeds the cats when the family is away. Like DUHHHHH!!!!! Did she not notice that one was missing. She didn't even ask my neighbour if she had seen her or not. So now I don't know if it was the sister that let Kitty out or what.
Anyway, hopefully the family will be back tomorrow and all this can get straightened out. I just hope that they appreciated what I did for their cat.

I'll keep you posted.