If the diaphragm in the fuel pump is torn, fuel will gravity feed through the pump and impulse line into the crankcase. It's rare with these pumps, but not unheard of. It's the only thing I can think of that would cause it to fill up while not running.It wouldn't be a fuel pump issue because you need a running motor to work the fuel pump. The fuel pump runs off of the impulse line from the bottom of the crank case.
It could be the needle and seat might possibly be stuck too. But when they stick, the floats hang down so the seat will be open allowing fuel to flow.
Rip down the carbs and clean them . I would start with the choke plungers.