when you are done for the season using your 9.9 kicker motor and will not be using it for 4 to 6 months depending on the weather, is it best to just add stabil to the gas & oil mixture or unplug the fuel hose and let it run out of gas ?
It is best to start the motor and then disconnect the fuel hose and run the engine out of gas. This will drain the tiny orifices in the carb, but you'll still want to drain what remains in the carb bowl. If you don't drain the bowl, this fuel/oil can and will plug things up in the spring.
Stabil will slow the oxidation rate of the fuel and help keep it "fresh", but it won't do anything for evaporation. Anything left in the carb will likely dry out and turn into sludge over the winter.