Luckily she freed herself just as I opened the cage to get her.
I looked at her and her mate and saw that their claws were overgrown. Both had some claws that could have caught and hung them up on the cage or the cocofiber in their nest.
I needed to check them more often, but did not want to do too often and spook them, especially since I wanted them to breed.
When I caught them to trim the claws, I found that her front middle toe was dark gray and the claw was missing. My guess is she got herself caught on something and struggled to such a degree that she pulled the claw out from her toe

I hope my cutting their claws did not spook them to stop mating.
I rebuilt their nest and the hen was busy in the nest.
I'm hoping that their 3rd clutch will be successful.