That's a sure sign of egg peritonitis. The albumen like material has almost a cooked like appearance. It's caused by the reverse movement of albumen and E. coli bacteria from the oviduct into the abdomen.
Regression of the ovary can result in the leakage of "free yolk" into the abdomen.
Very rarely results in death, unless the yolk travels through the air sacs to the lungs, which would cause pneumonia.
Usually occurs if there has been an acute illness or an injury, sometimes if there has been a forced molt.
I've had a few of my hens (Melanistic) have this condition. They survived but layed shell-less eggs, deformed eggs and for whatever reason I wasn't able to determine, layed eggs year round.
I believe it's a genetic defect of the reproductive system.
As far as feed is concerned, I would get them on a complete balanced feed of at least 24% protien. Adding oyster grit free choice is also a good idea, which, a complete commercial feed should have ( calcium carbonate ) added to the feed but sometimes, it isn't or not in high enough concentration for maximum absorption in the digestive processes. HTH
