Neighbor's Intellectually Disabled Relative (?) Keeps Wandering Into Our Yard. Worried About My Dog.

Location: Georgia

My dog doesn't have a bite history or anything, but she has growled at men who she doesn't know who come into our yard when we're not outside. (She's never done it to our other neighbor's children if they come in to get their drone and just tries to steal it from them lol.) For example, a water meter guy once let himself in back there and then came and knocked on the front door and asked us to put her up because she was barking at and jumping around him and giving him lip. She is a big girl, 82lbs, so even a "little" bite could potentially be catastrophic.

A few months ago our neighbor had a very obviously intellectually disabled relative (or possibly unrelated) move in. He stands at the fence and tries to beckon my dog over, but she avoids him. We tried introducing her and he was clearly making her uncomfortable, getting down in her face and grabbing at her. She didn't growl or anything at that point. Then he started hopping the fence and coming into our yard. A few weeks ago I heard something happening out there and came out and he was chasing her around the yard, she had her tale tucked between her legs and was trying to get to the dog door and he was blocking her path. I texted my neighbor and asked her to talk to him, and she said she would.

This has happened a few times since, most recently my husband was doing lawn work out front and went to the shed and found him standing on our side of the fence and our dog was standing in the middle of the yard and growling at him. She calmed down and went inside when my husband came back there. My husband talked to him and told him that he needs to come to the front door and ask for permission to come over, and closed the dog door. But then my husband went back there again and he was sitting in our yard.

I am really, really worried about our dog potentially biting him. We have a high fence and locking gate in the front, but the fence with the neighbor is only four feet. I'm not sure if that's relevant. We have now talked to the neighbor twice and sent multiple texts, and both my husband and I have talked to him directly. We have started closing the dog door when we aren't home (which sucks for my dog, tbh). I have so many people who can attest to the fact that my dog is well behaved, but I'm not sure it would matter if she bit him. My husband suggested maybe getting him some treats he can toss my dog over the fence, but I'm afraid that encouraging unsupervised interactions is a bad move.

My question is, what is our potentially liability here? If something happens with my dog, I'm assuming that animal control will take her and I'm terrified they will try to put her down. I'm also worried about getting sued. Is having documented proof that we have told him multiple times not to come into our yard, and that he does it without permission, enough? We are getting a camera installed. Do we need to pay to have a new fence put in? Is our being aware that things could potentially escalate damaging to us?

(Also because I forgot to add, our dog is vaccinated and registered and wears the license tag on her collar.)

ETA: Thank you everyone for the advice! Our next steps will be adding a trellis to the fence (neighbor gave permission) while we go about getting a proper fence installed, and my husband will set up the camera as soon as it arrives. I talked to someone at DHS earlier and will get a call back, but they advised in the meantime calling the non-emergency number next time it happens. I will be talking to my neighbor in person this weekend and letting her know I will have to call the non-emergency line next time we see him in the yard.