Keep her or turn her in to a no-kill shelter or a rescue. You could also put up signs asking who in the area has that cat, or lost it?
Leaving her outside to have kittens and then breed more kittens is just not responsible, although I realize it's not "your" cat.
Personally I would at least get the shots into it, and get it fixed. I wouldn't just stop feeding it though, I'm too much of a softie for that too.
Just the suggestions I can come up with right now.
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