The only two animals that will regularly try to chew-off are raccoons and mink. Both can be prevented by using either a #1 trap, or a double-jaw trap, or a very large trap like #3 that catches them up high.
Muskrats only wring-off, they do not chew. This is easy to prevent by using a larger trap of #2 or bigger, since it gets them up higher on the leg where their bones aren't so lightweight.
I've never heard of anyone ever saying that a fox chewed itself. Canines don't do that.
The key to late-in-the-day canine checking is to place your sets in such a manner that the fox/coyote can maneuver himself around toward a "hideout" such as behind some brush or next to a log or lower in a ditchway. So long as the canine does not feel threatened externally, they will simply lie down and wait it out after pulling and realizing that they cannot get free. You can use either a longer chain, a slide wire, or a drag.
