If dogs can dig under so can fox, raccoon, rats, you name it. Either dig 2 feet down to bury 1/2 inch hardware cloth around the entire coop and run or spread a 2 ft wide hardware cloth apron. No chicken wire, it isn't made for predator protection, only to keep chickens in. I swear chickens are the only animal unable to rip through chicken wire.and the dogs dug under the fence once they saw the chickens were loose.
Maybe THAT'S why we call it "Chicken Wire!"