What is the legal time that a stray has to be held at the local animal
control agency before it can be adopted? Generally, the law will find that
if you made a good faith effort to find the owner within that period and
notified animal control and other humane agencies, then that animal can be
considered unowned and can be adopted by you. YOu now have spent money on
this animal and it is listed in your name at a vet which also provides
provenance of ownership should any legal issues arise. The tricky part is if
a previous owner actually did spend money on vet care or an adoption fee for
the animal and it scooted out the door shortly thereafter and then wandered
for a while before he found you. If that's the case, then he need to
reimburse you for your expenses for his animal before it's returned.

I personally would go take a look at the poster just for my own peace of
mind. If for whatever reason the dates were right and the animal looked
right, I would give the number a call. BLOCK CALLER ID! *67 I think. If,
after you've asked a few pointed questions (like why was this cat in
horrible shape and unneutered) you determine that this WAS their cat, then I
would have no qualms about keeping him if his absence wasn't just a freak
accident. I would also attempt to educate the owners on cat ownership and
care-- for the subsequent cat that they are sure to adopt. You only hope
you reach them. That's why I suggest blocking the caller ID. If it turns
out to be their cat, and they are assholes, you don't want them having your
phone number. You have no idea what a ****ed off idiot with your phone
number and too much time can do, and making police reports is a hassle.