Re: run motor dry or use sta-bil and leave connected
I believe if you look at the OEM owner's manual for your engine, it will specifically tell you not to run it dry for the reasons given above. Anyone who tells you to run a multi-carb'd 2 stroke dry doesn't know what they're talking about.
Single carb'd engines are a different story, but you can follow the same procedure with them as well. Some think that even with single carb'd engines, it's best to leave the fuel in the carbs because it doesn't allow the rubber parts to dry out, plus, even if you 'run it dry' (or drain it), there is still residual gas in there which is certain to dry up and possibly leave residue.
IF (big if) a manufacturer recommends removing fuel from a multi-carb'd engine, it would be done by draining the system, not running it dry.
There are excellent winterization (i.e. lay-up) guidelines in the FAQ section.