Skunks can differ a lot in their behavior, but I just wanted to say, the skunks we have come around have rarely ever gone after a chicken. They can dig, but usually they go after eggs. We even have a skunk named Denarius (wild) who will snuggle up with our chicks in the nest boxes when nervous. He doesn't spray me, attack them, or cause any damage next to the egg eating. I go out early enough and shut the coop up and he can't hurt any of them. Broody hens are locked into secure wire crates with their chicks for extra protection if outside of the main chicken roost.

Foxes, however, are determined, intelligent, and good diggers. They will come back, day or night, and catch a stash of chickens that they bury out in the woods for later use if they ever go hungry. They learn human behavior and know how to avoid being caught and so are much trickery then skunks, which are bad jumpers, terrible runners, and seem a little slow in the head sometimes.

Denarius is not the first skunk I've had around. His mother (I think it was his mother) Black Star only killed one chicken, a mother bantam hen, and I'm pretty sure it was out of desperation to feed her six young kits. Otherwise, she too only dug into pens to go after eggs. She memorized where they were laid and returned to these areas. She also ate chicken food and cat food, as well as any insects in the area.

Skunks are not built to be hunters but opportunistic omnivores. Burying the wire down into the ground a foot or so is a great way to stop digging. You can also try putting stones around the border, locking the chickens up earlier (before dusk, using treats to lead them inside), and laying down wire inside the run, covering that with dirt and grass seed so that the hens can still forage but nothing can dig inside.

I hope you can stop whatever it is coming after your flock. Best of luck!