I never close the pop door, they can go in and out of their coop at will.
Our current run is a 12' by 7' chainlink dog kennel with hardware cloth all around the lower part, extending outwards over the ground, with cinder blocks on top. Above the hardware cloth is chicken wire attached, that extends over the ceiling, with roofing panels over the ceiling wire. There are also roofing pieces that surround the whole thing and go straight down into the ground about 18". No predators have gotten in, we have raccoons, coyotes, weasels hawks and random dogs and cats.
One time we noticed that something, probably a raccoon, had pulled a section of the outer chicken wire apart, but then it ran into the chainlink and couldn't get through.
We're working on building a bigger yard attached to this one, about 16' by 36'. It's about half done and has chicken wire around the sides, with a layer of hardware cloth going up 2.5 feet and extending outwards over the ground 1.5 feet. Above the hardware cloth will be welded wire attached to the outside of the chicken wire up to the top boards, and on the inside attached to the lower boards will be aluminum panels dug into the ground about 1 ft. The ceiling will be chicken wire attached to a PVC frame. The gates are already attached, really secure "dutch door" style of wood frame covered with hardware cloth, tight-fitting.
When this gets done, we're going to make a pop door that leads into the big yard from their current yard. That pop door we will be closing at night, because the walls of the big yard will be secure, but the roof will be just chicken wire that a creative raccoon could get through, if it doesn't mind falling 6 feet.