Two stroke engines are reversible relatively easily---little more than ignition adjustments required. I recall some type of three wheel utility scooter from long ago that obtained reverse gear by stopping the engine and restarting it in reverse rotation.

On a four stroke, it it a lot more difficult. It requires a different camshaft. This was done in several models of Fiat Abarth in the 60s. The engine of a Fiat 600 turns clockwise, as do nearly all other cars. For some reason, the engine in the Fiat 850, while very similar otherwise, rotates in the opposite direction. This led Abarth to make special camshafts to permit use of the 850 engine in a 600. A couple of years later they went in the other direction to convert a pushrod 124 engine (normally clockwise) for use in an 850.

Your problem is most likely "running on" also known as "dieseling" caused by an ignition source other than the spark plugs, such as carbon buildup or a sharp metal edge in the combustion chamber that acts as a glow plug. In this circumstance it is possible for the engine to rotate backwards, which will often cause a cloud of white smoke to come out of the carburetor(s) Fuel injection engines are not prone to this as there is a positive shutoff of fuel when the engine is turned off, unless, of course, you have a bad (leaking) injector.

Running on is bad for the engine, as the motion is violent and jerky instead of smooth and regular. I have heard if it lasts for more than a few seconds it is a good idea to stifle it by stalling the engine out by gently letting out the clutch in fourth gear with your foot on the brake.