I remember last spring I thought I had egg eaters and someone said this too. You told me I probably only had opportunists and you were right. Turns out then I had brittle shells because I was feeding layer but no extra calcium corrected that problem and no more broken shells in the nests.
Sorry, this will likely be a long post.
I grew up on 40 acres with 20 acres of Prune trees. We moved when I was 17 and we always had chickens. We also had Rabbits when I was very young, Pigs and Cows\steers for meat. One of my first chores was collecting the eggs and then getting them their food and water. It was a huge shock when we had to move to the City and I had to start eating store eggs...Gross(it was the 1970s). In all of those years growing up there was never any talk of Egg eating hens.
When I was in my 20s, my Father in law bought a place near us that had about 15 acres with a pasture and an Olive grove. The place came with chickens and my Father in Law was old school--he did not feed them anything but the odd bit of scratch. He started finding broken eggs and would shoot any hen that he found with egg on her beak. That one was a dreaded Egg Eater! I could not convince him to stop. He went on vacation and we took care of the place for a month. I picked up some chicken layer and got them laying regularly again. That lasted until they returned from vacation.
The hens lasted another several months and then he killed the last of the Dreaded Egg Eaters.....
Poor hens!
Egg eating hens are so rare that most will never have one. Eggs will break and the hens will eat them. It is normal hen behavior to peck an egg to see if it is viable for hatching. If it breaks she will eat it. Hens close enough will eat it too.
The point to all of this is that 99plus% of egg eating is an indication that something is wrong with the egg. Correct the problem and there will be no more eggs eaten.
There will be broken eggs and Pullets\hens just starting back to laying or reaching point of lay will have eggs that are soft shelled or broken. When this happens it is normal for them to eat the egg.
To correct egg shell problems:
Give them Calcium(adding food grade Diatomaceous earth to feed is a good way to add calcium--then give them free choice oyster shell after the eggs are hard again)
Check for Mites, lice and worms
Give them a good pro biotic every couple of weeks
Give them vitamins every week of so
Cheers!