What the heck is this?!?

[Green Acres farmer]

This one is about a year and a half old.

 

[Green Acres farmer]

Yes, it's a real thing. How old are your birds, it could just be a glitch.

She is about a year and a half. I just looked up membrane tail. It’s what it looks like, but the shell is hard and the tail is curled. Strange.

 

[chickengr]

maybe your hen tried to lay another egg before this one and she didn't make it. I once found a soft shell attached to the egg.

 

[aart]

Pig Tail!!
Was my first thought.

Yes, it's membrane that didn't get formed properly, so didn't get shelled.
Probably a glitch and may be a funky pre-molt egg.

This one is about a year and a half old.

If you live in the northern hemisphere, she should be ramping down egg production for molting and winter break.

 

[KingD]

An elephant is most certainly going to hatch out of that egg.