I have 50+ free-ranging birds, and there is no way I could possibly make a run large enough to house that many without hygiene problems. Three years ago, I had problems with foxes stealing some of the birds, tried shooting them onsight, but they seemed to know when I was waiting, so dug in some coil-spring traps, set them with some of the dead bird, and in a week caught/dispatched all five foxes. I attach a cowbell to the chain, and can hear when they're caught from inside the house. Flash forward today, no new predators have moved in, and I'm fox free.
If they're getting that close, I'd say go for the gun.