My brother told me he heard that chickens need to eat the eggshells to keep producing eggs.
I found it odd. I could see that eating eggshells could produce healthier/stronger eggs/chickens. But I wouldn't think it would be necessary to production.
So, I bring the question here.
Backyard flocks are certainly fed eggshell for the calcium. They must be well crushed so the birds don't start eating whole eggs before they are collected, though, which can happen and is a PITA to stop once they get going. We like eating eggs, chickens LOVE eating eggs. Which sounds kind of bizarre but it's intinctive to "clean up the nest" so a predator doesn't get attracted to it.
Larger flocks will mainly be fed crushed oystershell for their calcium needs, or any other good source of calcium that can be incorporated into their layer feed.
Calcium is definitely necessary for good egg production. In pre-present day chicken times a hen might have laid a few dozen eggs a year. With domesticated chickens we want as many as we can get, which can have chickens laying an egg every day. So that's ten times or more what they may have laid when they were wild. You can take only so much calcium from the bones and blood before it's not good for the chicken. When the hen startd getting to that level, the eggs simply come down the reproductive tract with no shell on them, only the interior membrane. That's the reason they need the supplemental calcium.
Egg laying chickens need calcium to make their eggshells. A standard chicken feed ration may not have enough calcium to replace what they put into their shells, resulting in thin, easily cracked shells. However, there are other sources of calcium. Most people buy ground oyster shell, which is extremely cheap, and feed that ad libitum. If you have a dairy cow, the leftover skim milk you have after using the cream and making butter is also a good source (let it sour/clabber first to add even more goodness). Eggshells are an option, but kind of a hassle. Most people figure it's a good idea to crumble them up so the chickens don't get in the habit of breaking egg shells with their beaks, and they're messy to do that with. A hen who learns to eat eggs is good for nothing but soup.
Also, my experience is that chickens that get to spend a lot of time outdoors, grazing on bugs and grass, seem to get enough calcium in their diet that weak shells generally aren't an issue. I do keep oyster shell out for mine, but they rarely touch it.