How current flows in a circuit as per Kirchhoff's law if the voltage dropped = voltage applied
The situation you’re describing is the ‘steady state’, where the 9V from the battery exactly matches the 9V across the load.  But there’s only 9V across the load because a current is flowing.  The current won’t suddenly stop flowing because that would create an imbalance between the 9V from the battery and the less-than-9V across the load, which is obviously impossible.