If the Yogurt has mold in it or smells bad and it's very old then it can make you sick to your stomach and could cause food poisoning.
But if the Yogurt is just a bit older than the expiration date and it has no mold or doesn't smell bad and it has been refrigerated all the time then the old yogurt should not make you sick.
If it does have mold in it or smells bad then throw it out and don't risk making yourself sick or getting food poisoning.