Same hen as this other thread? Did you deworm and treat for Coccidiosis?
https://www.backyardchickens.com/threads/what-is-this-in-the-poop.1499537/
Being hunched up and finding what you think is shell membrane in the nesting box, I would wonder if it's Albumen (egg whites) that you saw. She may be having a hard time expelling another egg. If you haven't given her a Calcium tablet this morning, then I would.
It sounds like her crop is not emptying - this is often a symptom of an underlying condition. If she's struggling with reproductive issues, this can cause the crop to slow due to inflammation, infection, blockage, etc.
Make water and a little food available for her.
If you have any antibiotics, I would give those too to help prevent infection since you don't know if the membrane broke before or after she expelled it. Amoxicillin would be a good choice.