It's possible that she may have fatty liver and/or fat in the abdomen along with the Salpingitis. I do not know if a fatty liver can be felt as a mass. Sometimes Salpingitis, cancer, tumors or eggs can be felt as a mass in the abdomen.
You will have to do some research/reading, but sadly...
I'm not a vet, but would have to say that your hen has Salpingitis (see the links and information in my previous post).
Unfortunately, there is not any real treatment for this. Sometimes antibiotics can help with infection, but usually when you start to see symptoms and poop like that the...
Photos of the poop would be helpful.
From this description, it sounds like she has Salpingitis or "lash egg". Take a look at the links below to see if anything looks familiar.
http://www.the-chicken-chick.com/2014/12/salpingitis-lash-eggs-in-backyard.html...
Can your vet perform an xray to see where it is?
If you are feeling an egg shape under the intestines in the abdomen - then it could be a tumor, an actual egg or some other mass that is in the abdomen. This would indicate a reproductive/internal laying disorder like Egg Yolk Peritonitis...