Like I said, A LOT of work, to build a proper and safe wood frame and wire run. If you go that way, the run will have to have some kind of cover, wire, or whatever. Because a ground predator is not only capable of digging under and in. They can climb and go over in a blink of an eye. Reading about what's involved with constructing regular wood framed run, I'm more than happy with the way I went. Digging post holes, burying aprons, the heck with all that.
I have hawks, eagles, owls, everything that flies, short of a pterodactyl. I provide my birds with ground cover to hide in. The coop itself, a big brushy area behind the coop. There are a few pallets on top of some cinder blocks, with tall grass growing around them, for shade and cover. Chickens learn and react to the airborne threats. I've even seen them react to, what must be hawk warning cries from crows, and haul butt to cover. That said, I did lose a bird to what must have been a hawk, about 3 yrs ago. But, I believe the chickens used that, as a learning experience. They are well tuned into their environment now.