Other questions on this site have addressed the fact that unwashed eggs do not need refrigeration because they are protected by a "cuticle". Washing removes the cuticle, and therefore washed eggs need to be refrigerated.
If unwashed eggs have already been refrigerated for a few weeks, and are subsequently left out unrefrigerated for a another week or two, is it still safe to use them? That is, does refrigerating the unwashed eggs remove the protection of the cuticle in some way, or otherwise make it dangerous to subsequently leave the eggs unrefrigerated?
Edited to add: Since originally posting this question, I have come across the following claim:
In America, food safety officials emphasize that once eggs have been refrigerated, it is critical they remain that way. A cool egg at room temperature can sweat, facilitating the growth of bacteria that could enter the egg through its porous shell.
From the phrasing of this statement, it's not completely clear to me whether this principle ("once eggs have been refrigerated, it is critical that they remain that way") only applies to washed eggs (the context "in America" suggests that may be the case), or whether it applies to all eggs, whether washed or not.