Update: today when bathing the hen and gently picking at the black and yellow tissue, a good amount of it broke off. There was a little blood when this happened. I left the remainder on the hen since trying to pull it off would have caused much more severe bleeding. I lubricated the area and applied antibiotic cream. After this large dead mass broke off, the prolapse went back into the vent by itself. The hen still looks like she is straining a little, maybe the remainder of the dead tissue still feel like a small poop. The hen was awfully tired after all of this, haven't seen her that tired before. She is still eating and drinking well though. I didn't think she would make it, but after seeing about 75% of the mass break off and the prolapse receding, I think she might make it if she survives another couple days. Hopefully she does not get an infection.