Draining is always the best possible approach.
You add stabilizer when you put fresh gas it. It's purpose is to stabilize the gas. If the gas is old its beyond help, so putting it in (or adding more) is of no value.
I agree, but if you can't easily drain the gas from the carbs, which I can't on my snowblower and motorcycle, a storage additive helps. It prevents tarnishing which would plug up the small passages preventing spring time start up. Tearing down and cleaning the carbs are a pain in the butt.
There are different forms of stabilizer additives.
STA-BIL Storage - Keeps fuel fresh for long term storage – up to 24 months.
STA-BIL 360 Protection - Ultimate treatment and protection against Ethanol blended fuels, Non-Ethanol Fuels & condensation.
STA-BIL 360 Marine - Ultimate defense against the harmful effects of ethanol blended fuels.
My snowblower I'll add it to my fresh 2 gallons of gas beginning of season. I haven't used any more than that in a season.
In my motorcycle I add directly to the remainder in the tank at the end of the season.
You can successfully add it to 6 month old gas.