Anyways, here's some tips if someone left a stray cat near your house and you wanna help!
Live traps are your friend. Put some cat food or tuna in there and wait.
If you don't want to keep the cat yourself, you can either take the cat to the nearest no kill shelter or keep it for a bit and post somewhere about rehoming it (Always have a fee, if you give away a cat for free it's more likely to end up somewhere bad)
If you DO want to keep the cat, then some tips for handling it; scruffing (although some cats are uncomfortable with it and won't go limp, in this case, don't do it obviously) Can help, and wrapping the cat in a towel can help calm it down.
If the cat has fleas, the cheapest and easiest option to at least get rid of some of the fleas is to bathe it with dawn dish soap, make a ring of it around the cat's neck so the fleas don't crawl up to it's head to escape.
Common and obvious problems a cat can have are ear mites and eye problems. Obviously, you can take the cat to the vet for these things, and you should probably do that anyways for a check up. (If the cat is constantly scratching it's ears specifically and tilting and shaking it's head, and has more earwax than normal, that will tell you it probably has ear mites, and the eye problems are easy to spot) And if you would rather try to buy medication yourself, avoid the brand Hartz, because i've heard many horror stories about that brand, and even the vets I went to said to avoid it.
Every cat i've taken into my house has responded positively to having their own space for the first little while, a single room with a place to hide until they're ready to come out and explore.
To get the cat to trust you more, be very mindful of it's body language. If it turns away from you, don't continue to try to get closer. Literally just respect boundaries and you'll be way better off.
If there's issues, do NOT declaw the cat. That will only create more behavioral issues. If at any time (before the cat gets comfortable with living in your house) you feel in over your head, don't continue the cycle. Refer to tip #2.
These are not tips from an expert or anything, i'm just a person who's had lots of cats and is seeing way too many being abandoned in my neighborhood when I can't take anymore in. I know I wrote a few controversial things, but these are all things that have helped me in the past, and my cats are happy and healthy, trust me, they get everything they want.
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