I've caught a few coyotes thru the years, even lost one occasionally, but never saw evidence that any had chewed their foot off to escape. ?????? A toe twist off, maybe. Most of my losses were due to entanglement situations and trap jaws that weren't modified or didn't have cast jaws. Maybe I just haven't caught enuff yet.
I've had it happen once and took a good while to catch him after that, and have heard of it from others guys that trap around here. True the same on ones that twist their toes off. I was after a gyp this summer that kept scratching around holes at fence crossings and bumping traps. Never set one of or completely uncovered them but would just move along and not come to my side where the sheep were. I had caught a male a few weeks before she showed up and just figured that was her mate and she possibly related fence crossings to his disappearance. Maybe I'm giving them too much credit, she dang sure irritated me for a couple of weeks.