In an attempt (so far successful) to seal off Sally's escape routes from the run, we've created an elaborate cats-cradle lattice over the taller structures in the run. Even after we clipped one of her wings, she was hopping up on to the coop and then hopping onto the fence in order to get out. The last thing we need is a chicken on the loose, but we also didn't want to permanently affix anything to house. This was our compromise, and for $3 in string, it seems to be working.
It strikes me that this might work well for bird-of-prey proofing a smaller run.