Can't imagine a bird of prey getting a chicken from the run, though?
My only predator loss was coming home to find a small hawk pinning down one of my chickens inside the run, eating her, while the rest of the flock screamed in the opposite corner. Immediately bought some netting for the top, which had been "fine" for 2 years uncovered.
You said you're doing HWC across the top though right? As long as it's all attached securely that'll easily take care of any bird of prey issues.