There are two schools on fuel storage and they are both right, for different machines. The mistake is doing half of either.
Run it dry. Turn off the fuel tap, let it run until it stops, then drain the carburettor bowl from the drain screw if it has one. Nothing left to go off. Best for small equipment you will not touch for six months, and it is what I do with the trimmer and the mower.
Fill it and stabilise it. Fill the tank almost full with fresh fuel plus a stabiliser, then run the engine for a few minutes so the treated fuel is actually through the carburettor. A full tank has little air in it, so less moisture and less condensation on the walls. Better for anything with a metal tank that would rust, and for a generator you might need at short notice.
What does not work is the middle, and it is what most people do: leave a half tank of untreated fuel and shut the door. Maximum air, maximum time, no protection.
One thing worth knowing about running it dry: it does not empty the bowl completely on many carburettors, so a small amount is still sitting there. That is why the drain screw matters, and it is the difference between mostly working and reliably working.
Whichever you pick, do the whole thing.