You need to stop driving this vehicle and have it checked out right away.
Thats not dropping to "empty",thats showing No Oil Pressure.
It needs to be determined if its actually losing oil pressure or just giving a inaccurate reading from a failing oil pressure switch,instrument cluster and /or wiring.
What needs to be done first is have a mechanical gauge connected in place of the oil pressure switch and have the oil pressure tested to be sure its within specs.
if this is not done immediately and its losing oil pressure,driving the vehicle/running the engine will damage the engine...And it takes literally no time at all to damage an engine from lack of oil pressure.