@3KillerBs nailed it. Fix your drainage issues. Likely an “easy” task with a shovel, but could require something larger.
where are you located, in general? what type of soil are you dealing with?
in my location, western Ohio, I have flat, clay soil. Our coop and run are directly behind the barn and we have a roof over most of the run. Our coop is elevated 2.5’ above ground. The flat ground can be a problem. We ended up getting in 102 tons of dirt (yes, actual tons) and had a bobcat to push it all around to level it out...this fixed a lot of our problems, but we are still working on some of the drainage in smaller areas. We have gotten several loads of chipped wood, which is throughout the entire run. We also got approx 800lbs of sawdust from a friend that works in a manufacturing facility so the sawdust was free, and laid that down in the run under the chipped wood (before we got the chipped wood, of course). We lined the run fence with old, wide boards to keep the chipped wood inside the fence.
So,with water running through the run area, You need to divert the water. You’ll need to build up the run material bc of rain that will come in from the sides. Any chipped wood you use may mold, but should be more like a forest floor -just decomposing wood.
good luck