Okay here's my thoughts - It looks like the top part of the beak, you could say "peeled off " because there's still the bottom part - by the looks of the picture.
There's also mud and other debris in-between the two parts of the beak so I would take a Q - tip or toothpick to remove that.
DON'T...
I am sure you have seen were, when chickens are going to fall off the roost that they hold on with their beaks. My guess is that she broke her beak doing this.
Poor girl!
When you get a chance to get some more pictures, please do so and tag me @GirlsHuntToo and I would be more than happy to take...