Well, waddayano, Stabil makes fogging oil! Whoda thunk?
Of course they claim you should use it in two- and four- stroke engines. Well, actually they say motor, but we all know that's not correct.
Here's the thing - back in the early 90's, when I lived in Hawaii, I used fogging oil in all my two stroke motorcycle engines whenever they went into storage for six months or more; the cans even specified two-stroke use. The logic at the time was that the combustion chamber got its lubrication from oil that was burned along with the gasoline and parts (such as reed valves) needed to be protected from corrosion. Fogging oil coated everything nicely and kept everything lubricated. When I moved to Texas in 1994, nobody I talked to ever even heard of fogging oil. I went on deployments without fogging my engines. Oddly enough, they all survived just fine. Now, years later, fogging oil is on all the shelves and it is designed to be used in all engines.
The upshot is, if you like it, using it makes you feel better, and you aren't starving your kids to pay for it. I say use it if you want. As for me, I'm filing it under snake-oil.