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Center pivot on rig Control?

Is there any danger in “centering the pivot” of a control on a rig? And is there a way of knowing where the original position that the rigger placed the pivot was?

e.g the jaw CTL is usually placed somewhere in the center of the head. I know it would not rotate properly if I centered the pivot to the control but apart from that what would be the risk and how can I reinstate it(apart from snapping)?