Your hen appears in the photo to have a prolapsed vent with an egg stuck in it. (Intestines don't make that shape...that is an egg shape...which could be soft shelled).
If egg bound with prolapse, you have two choices. Attempt to treat it, or cull her.
Prolapsed vents are hard to treat. I personally would put the bird down as it tends to happen again, but that's me since I don't want to breed those genetics forward.
However, there are those on BYC who have successfully treated it.
I will give you some links as to what you could do in order to treat it.