Is it bad to run a 2 stroke engine out of gas?

Running a 2 stroke engine out of gas can damage the engine. The fuel level in the carburetor drops because there isn't enough gas flowing into the carb from the tank. As the fuel in the carb drops, less gas will be fed to the cylinder. Most 2-strokes will run fine or even better under lean conditions, until the excess heat melts a hole in the piston.