Deer snap traps and leave little sign.
Opened J-hook, sprung trap...I would have to looksee for myself at your equipment. Yes, a Coyote can open them up on a lunge or two, Coyote can pop jaws from frame & Coyote can bend trigger and bend bottom frame (been there with all of these).
If a person was going to the trouble of springing your trap and opening your J-hook, he would certainly steal the trap at that point. Possibly your J-hooks aren't completely closed or you may need to change your chain attach point. By that, center swivel your chain opposed to attaching to side. or vise versa. or Shorten your chain and pin 'em down? I would have to see how you have your footholds are rigged but still think Coyote and equipment are to blame.
If no blood pool or no distinct catch circle (which you didn't mention) it wasn't stolen. Cool down, SEE what you are looking at.
Uncle Buck, I rarely miss a Coyote nowadays with my equipment, but years ago I did. Same as you...equipment failure, trap sprung, chain extended, no catch circle, no critter. This happened often when I was learning how to Hold Coyote. Key word- hold. Proper size trap, proper tuned up trap, proper swivel and chain attachment, proper staking are all part of a system to go with proper set construction to HOLD what steps on the pan.
Just like getting a new gun & scope still in the boxes. There are certain details one must do to fine tune and match up gun, correct mounts, centering scope and finding the right ammo to constantly touch holes in paper. Now you have your equipment right and feel confident. Know what I mean? Same applies to each and every foothold trap you own.
If you have more question, feel free to ask here or pm me.