Have one hen in 20 that is giving a shell less egg or one with a paper thin shell every3-5 days? The last few have had, what I assume is, some of her lining covering it. I doubt she is comfortable with the situation and needs help, or cooked. All other hens have perfect eggs and rock hard shells. Also having trouble identifying the hen as they like to share boxes. Ideas?
Is this mass solid? Did you cut it open to see what's in there?
Could be egg membrane or tract lining over shelled egg.
Shelled egg can back up the pipe and be 're-membraned'.
I assume the greenish stuff is poop?
She definitely has some repro system issues.
How long has this been going on?
What breed is she?
Lipstick jokes notwithstanding, that
is one way to tell who is laying what,
but would be pretty hard to employ with 20 birds.
I'd look for a bird that is 'not acting right' with a swollen belly, maybe her stance is more upright with tail down and walking like a penguin.
Handling each bird, off roost after dark is easiest, and feel their bellies from below vent to down between legs might be a good place to start.