I know that a Muskrat can and will! and I have caught them healed up with 3 leg before!
No, muskrat do NOT chew their front feet off. They are simply delicately constructed and can twist off a front foot. The various styles of rat traps with wire bails prevent rats from twisting and losing a foot.
I have never seen foxes, coyotes, or cats chew feet, but lots of coons.
