These vases were meant to have a bronze grille or top to make flower arrangement on a low table possible. In several countries these are called Biedermeier bouquets, and a metal grill is needed to arrange them properly. The grill meant the top rim could be left unfinished. Somewhere along the way someone emptied the dry flowers from the vase, and chucked them in the bin including the grill. So if you have a low vase with an unfinished rim, it may have had a cage at one time.