Foxes are very creative, persistent and talented. They can dig, jump high, climb - if you have any weak area in coop or run, they will find it. We have foxes out here - suburbia but surrounded by Forest Preserve. They come out early morning, around dusk and any time during the day. I was coming home and decided to check the side of the house for blooming plants. As soon as I entered the passageway between the neighbor's & my house I saw a fox coming towards me -he retreated in a flash and leaped the fence in a single bound. He was mighty lucky - because the fence he jumped was where the pitbull lives.
I would strongly suggest a cover for your run. If you are using chicken wire - foxes and raccoons can go through it like it didn't exist.