The others are so right...your rooster didn't do this. Without pictures of your setup, it's very hard to tell where your issue might be, and you said there are no signs of where anything could get in. But might I suggest you look UP as well as down? There are so many variables and predators are able to exploit all of them....
Do you have trees around or close to your setup? A shed or garage? Raccoon or mink can use them as ladders and get in through small gaps at the top that you might not even be aware exist. They don't need them to gain access, though - they can climb right up the sides of the run. If it's a rat problem, they could be IN the coop or run even as you are out there investigating. They can (and will) hide in ground nests under feeders deep in the litter and you might never know they're in there. If your coop is tall, like mine, they could be tucked in the corner on top of a rafter and again, hiding in plain sight. No tracks around the setup could well mean they are already in there, hiding and sleeping during the day and coming out at night.
They can also peel back a small area of chicken fencing or chicken wire and because it's springy it can sometimes spring back and look like it's been undisturbed unless you look very carefully. At this point it's hard to say what's getting in or how, but you definitely have something in there and it's creating total carnage. A lot of people put aprons around their run fencing and skirts going up the run because it looks like the obvious place for predators to get in, but what do you have around the base of your coop? I have a skirt and apron around both. Photos in cases like this are so helpful.
