Care of RhodeRunner in diff. catergory...
It is certainly possible. But, if they are there is typically some evidence (sticky nest boxes, little bit of yolk dried on the beak/comb), chickens are typically not the cleanest eaters.
I have had a few egg eaters, and thankfully never had to put one down. To cure they I have used the golf ball technique. With a golf ball in the nest the hens will see that no mater how many times they peck it nothing is coming out. Shortly after they stop trying to eat the eggs.
I also had a hen that was eating eggs, but I was unable to find her nest. In her own time she stopped.
Finding the culprits and separating them from the rest of the flock until they stop eating eggs may be a good idea as it can stop the spreading of this habit.
Some people have said that egg eating comes from lack of nutrients in the birds diet, which I suppose is true. But, you should be able to judge how healthy the birds are (feathers eyes.)
Also, it is typical for the hens to eat the eggs after laid, so if she got eleven then she may not have a problem, or one hen is going in there and snacking later on. Sometimes it is a rooster that is doing the egg munching as well.
Hope she manages to clear up this issue.