The fuel bowl should be full of fuel at all times except when ran dry. The solenoid doesn't stop fuel from flowing into the carb, and will not prevent fuel from overflowing the carb in the event of a float valve failure. The solenoid, often referred to as a fuel shutoff solenoid isn't a fuel shutoff valve. It is an afterfire solenoid The purpose is to prevent fuel from being drawn into the engine from normal valve and piston cycling and then deposited into the hot muffler were it ignites, causing the dreaded bang.