Certainly a coop inside a completely secure run does not need any security.I'm thinking that the coop inside the completely enclosed run would have NO floor. In other words, the chickens would just walk underneath it and climb up into the roosting laying boxes and roosting bars. Any excrement would simply fall to the ground below where from time to time I could simply rake it from the ground. Their protection would not come from the coop inside, but from the completely enclosed run which will have both chicken wire and chain link fence and be enclosed ALL around. We have coyotes, fox, and a variety of snakes.
However, that simply means you need a skirt all around your secure run to stop diggers tunneling in.
Also, chicken wire doesn't really deter anything but chickens. Many people use hardware cloth (which is a tad pricey). Chicken wire plus chain link is definitely better than either alone, but something like a weasel would be able to get through an arrangement like that.