We just had one that remained uncatchable, except by small children. She had whip and chain scars diagonally across her body when she arrived at our house. She was terrified of any movement by humans within reach to the point she would pretty much drop to the ground. Once caught, she was fine, mostly. After a few summers of being played on by experienced teenagers, she was very safe and seemed to be comfortable around humans, but never cared to be scratched or petted. No bribery worked. Other horses being caught didn't worry her at all. If you cornered her (hard to do in large pastures), she'd run you over. We had her for 15 years, including one summer that she was up on the hill until the snow made her come in.

She became our beginner-rider horse. Send a small child to catch her with a string, and she would follow them anywhere. She would go around branches and trees, stop and nap while they played on her, or whatever.