I'm not suggesting this will happen to everyone who scrapes bedding into the run, but this is what happened where I now look after the chickens.
The holes you can see are rat runs. The paper and poop has formed layers, beneath which is all sorts of stuff. I'll be digging it out in the future...
I'm using shredded paper for bedding currently. It goes on a bedding pile. I can't in any honesty call it a compost pile yet. Paper on it's own takes a long time to degrade. One day I will add vegetable matter and get in there with a fork and turn it over.
Before I got involved with these...