Visio shapes have 8 resize handles. If I protect the height of the shape, only the handles in the middle of the left and right borders remain active. Now, is there a way to disable the left resize handle so that only the right one remains active?
The answer to that is no, although it would be a nice feature. If you want to expand a shape in a particular direction, you might be able to change it local pin position via the Size and Position window (View / Show / Task panes / Size and Position). IE, if you set the Pin Pos to Center Left, then dragging the right handle would expand the shape to the right. The default pin position is generally in the center of the shape.