A hen that eats eggs is probably destined for the stew pot. There is no way to train a hen not to eat eggs once they start. You can separate her from the rest of the flock but often she will cannibalize her own eggs as well which makes her useless for anything except meat.
If the hen eats broken or leaking eggs that is OK but if she is breaking open and eating eggs she should be culled from the flock. This behavior can spread to the rest of the flock and cause major problems. Once the hens recognize the eggs as a sourse of food they will continue, leaving you with no eggs and if you breed hens, with no viable stock for the following spring.
We tried to herd all of the sheep into the pasture, but one sheep strayed from the flock.
Eat them?
Yes. A setting hen should be isolated from the rest of the flock for the safety of the eggs, resulting chicks, and the brood hen, herself. Chicks have been successfully hatched without taking this precaution, but many who've done it have had problems resulting in dead or injured birds and low hatch rates. Results like these make it not worth the risk.
A value separated from the rest of the data is called an outlier
Normally they flock together in trees to roost.
Italy is separated from the rest of Europe by the Alps.
The Alps separate Russia from the rest of Europe.
You have not said how many chickens you have altogether. Chickens die for many reasons and not always from communicable disease. Poor nutrition, illness and predation. A hen being pecked by the others weakens them and then all they need is a minor illness to weaken them even more. Generally, I would say if the rest of the birds are acting normal and healthy then you would not have a problem eating the eggs. If they are all acting sick, then you may want to leave off consuming the eggs until you figure out why they are ill.
She is brooding which means she is going to try to hatch eggs into chicks. Some of the other hens will lay eggs near her and she will roll those eggs under herself. If you have a rooster in the flock and want some chicks you should let her stay where she is but if your flock has no rooster then take the eggs away from her.
outlier
The Himalaya mountains separate India from the rest of Asia.