Answer
When the supporting rope is vertical, S is zero. The tension and the weight are both vertical, and cancel each other.
If the rope were horizontal, S would point such that its vertical component is equal and opposite to mg. Its horizontal component would be equal and opposite to the rope tension T.
If the rope tension T and the force S were both horizontal, there would no way for the sum of the three forces to equal zero. The weight, mg, points downward and either force S or T must also have a vertical component to cancel that vertical component.
