A fox caught the night before will chew his leg off before you get there in the afternoon or evening, so yeah, they need to be run in the morning IMO.
This kind of misinformation is what grinds my gears. I have never once had any animal chew its own leg off. I have had fox that were asleep in the trap when I got there, they couldn't be more relaxed.
Animals chew on feet not to escape the trap, they do it because their feet go numb. If you use the correct sized trap they don't even have room to chew on their feet anyways.
