Yogurt was originally a food preservation vehicle.
It is quite acidic and if unopened and refrigerated it can stay good for a very long time.
The pasteurized, inoculated, milk is allowed to ferment in the container.
Foreign bacteria don't have much chance to get in and if they do the yogurt culture crowds them out and the acidity kills them.
Greek yogurt, with its lower moisture level, stays good even longer.
I have had very old yogurt from time to time (months past the expiration) and it has only ever gone bad in one of two ways:
Either it went moldy or the yogurt's own bacteria was allowed to work for too long and the yogurt was too sour and not creamy anymore.
If the yogurt isn't moldy then it is probably fine. If it has continued to ferment then it will be more sour and possibly broken but not unsafe.