A prolapse is pretty easy to see since they is reddish pink tissue sticking out of the vent. This can attract pecking by the other hens, and any hen with prolapse should be separated to avoid injury. The picture below shows a mild prolapse. Here are some links about egg binding and prolapse to...
With those symptoms, she could also have had coccidiosis. With chickens it is sometimes easier to rule out the problems if it doesn't look so obvious. That's the good thing about this forum--many people can give advice.
It sounds like she may be an internal layer by her laying the piece of flesh that could have been a "lash egg." I'm not an expert on that, so I would still suspect that she could be egg bound. I also agree that a dose of calcium would be good for her. You can insert a finger 1-2 inches inside...
I have occasionally been looking at this thread, and I would just like to mention that reproductive problems such as oviduct cancer, ascites, egg yolk peritonitis, and internal laying can all look similar to egg binding. Many times they will walk like a penguin too. Chickens usually will not...
If you are trying to stop laying, they should be in a dark space or covered cage for 16 hours a day, so she could range with her friends for up to 8 hours daily, but during some of that time she needs to be eating her normal feed. Lowering her feed ration below normal can have an effect on...