The nipple on the bottom of the carb bowl is the drain. Opening the screw next to it in your picture will drain the fuel from the bowl. There is also an overflow standpipe in the bowl which will drain excess fuel in the bowl, such as when the petcock is left on. The tube connects to that nipple and is routed behind the engine and ahead of the rear wheel on the right side, kind of behind the battery box. It's purpose is to route the fuel to where it can just drip on the ground (or garage floor) instead of dripping on the engine.
When you forget to close the petcock it is imperative that you check your oil for fuel contamination. It is possible for that excess fuel to make it through the intake, into the cylinder with the open intake valve, and past the rings into the crankcase. If there is any doubt, change the oil.
