Do Eggs get stale?

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I know eggs can rot and stink, but can they get stale and if so, how long does it take. I am an egg lover and since I eat 2 eggs every morning, I buy 4 doz at a time. My wife can eat for the first couple of days then she cannot tolerate them. Although, she can eat eggs from other places. Which caused this discussion. Is there a way to determine if they are not fresh? Canned or jarred food takes a couple of years to go bad, arn't eggs sealed like those?