Briggs and Stratton recommends that its engines are run until they stop from lack of fuel, before storage (e.g. during winter). Craftsman and Ryobi recommend that engines have the fuel "removed" from the carburetor before storage. I haven't checked any other owner manuals, except Honda which provides a drain plug in the carburetor float bowl and recommends that fuel always be drained before storage.
I have always made a point of running most 2 strokes until their carburetors are empty, because otherwise the fuel dries up during storage, leaving the oil behind, and the oil is likely to temporarily block the main jet and make starting difficult. That practice was widely recommended back in the days when I used 2 strokes. Of course you make sure to do this at light throttle with no load on the engine, to ensure that high temperatures do not develop for a few seconds as the mixture leans out. I personally would not run a chainsaw or motorcycle engine dry in that way, because those are very high performance engines, which could be adversely affected by lean mixture.
