In Skyrim while doing the quest for Clavicus Vile, if you refuse to keep the axe, but then speak to Barbas to interrupt him while Vile is telling him to "get over there", Barbas will not teleport to his place at the statue. BUT, you get an extra line of dialog from Barbas that you don't hear if you let the dialog play out without interruption. Afterwards, the statue of Clavicus Vile disappears completely and Barbas just continues to wander around the cave in dog form.