The worst thing that could happen (since modern freezers have a partial defrost cycle to eliminate ice buildup) is that, over time theres some texture change due to ice crystals.
But this even happens with ice cream which is designed to be frozen. Have you ever had ice cream which developed a sandy or gritty texture if stored too long? It can also happen if the store didn’t handle it properly prior to sale. Ive brought home containers of ice cream to eat the next day and they already had that gritty mouth feel. Mishandling during shipping or by the store did that.
It didn’t go bad (as in spoiling or souring) and isn’t dangerous but you sure don’t want to eat it since the mouth feel is SO unpleasant. But if you melted it and used as a sauce over berries it would be perfectly fine and safe to eat.
Any properly frozen food doesn’t really “spoil” in terms of SAFETY for eating. Its the texture, flavor etc. which are spoiled. Freezer burned meat is not dangerous to eat. The reason you don’t eat it or cut off the affected parts is because it’s too unpleasant to eat otherwise. But safe nonetheless.
Same thing with yogurt. Ive frozen yogurt before with no problem. I just know not to expect it to be all nice and creamy and yummy if its been in there too long.
But the distinguishing feature which qualifies yogurt as “Greek” has nothing to do with what country produced it. The process for Greek yogurt drains off more moisture than conventional which is why its thicker and creamier . Its just more dense. And that also costs more.
But less moisture lessens the likelihood of ice crystals forming (somewhat)