This looks like she may have an oviduct infection. Have you cut any of that open? If there is anything that looks like yolks, for what ever reason they are backing up in her uterus. If its all just gunk and such, its definitely infection. You might start her on Amoxicillin for 7 days and see if she is better.
Hi, in addition to the Amoxicillin recommended by @TwoCrows, I would recommend you really, really limit the treats. With a balanced feed, there is no need for scratch, corn or other goodies. Good luck with your flock!
Looks like lash material. It isn't necessarily a death sentence. I've had hens lay them and they are still alive and well. One will be 6 years old in two days and she still lays.
I hope your chicken gets better. I'd do what @TwoCrows suggested though, and just scramble and feed the chickens their eggs back until the day after you're done administering it.