I don’t know the correct technical term for that. When does it happen and why? How can this opposite rotation be sustained? Ignition timing would be totaly wrong. Also, why is it so bad for the engine when it happens?
Are you talking about the engine running in reverse or just turning…
…like if the transmission was in first or some forward gear and the car forced backwards?
I do believe that it happens when the point of ignition is to close to top dead centre. I saw it happen to a fella at the traffic lights on a Montessa motorbike.
Piss funny.
He went to take off forwards but went backwards, luckily noone was behind him.
The engine of the Lamborghini Muira had to be made to run in reverse to the way it was designed IIRC because of its orientation in the car. It was done by adjusting the timing of the engine. How do they do that 
Νο! Let’s say that the crankshaft normally turns clockwise. You have just parked the car and put it in neutral. You then turn the ignition off. The engine’s revs drop as usual, but then, instead of coming to a stop, the crankshaft starts turning in the opposite direction!
A four-stroke wouldn’t run - the whole induction-compression-power-exhaust cycle isn’t self sustaining run backwards.
A two-stroke engine, however…
If I wanted to change the direction of rotation for most four stroke automotive engines I might have to take at least the following steps.
[ul]
[li]Cam - Easiest way is to grind cams that give the proper timing when going in the opposite direction. [/li][li]Ignition - With a typical distributor it might be best to swap the helical gears so the rotor goes the same direction with the engine going the opposite way that it was designed. [/li][li]Oil pump - This is a tough one with most engines as you may need a redesigned pump to flow the right direction with opposite engine rotation. Most use a meshing gear type pump with one side driven by the jackshaft or crank. [/li][li]Accessories - engine driven accessories will have to be mounted or altered so they work correctly with opposite belt rotation. [/li][/ul]
Say, any aviation mechanics here? How about Lockheed P-38s where each prop went in an opposite direction. From the pilot’s POV the right prop rotates clockwise and the left counter clockwise. My WAG is that the engines were identical and both went the same direction but the reduction gear cases were different so one has an output shaft going the opposite way but I have nothing to base this on.
As I recall, back in my hot rod days (late '60s, early '70s), hot rodded automotive engines that were used in boats ran in reverse rotation to their landlubber cousins. Why, I don’t know (something to do with the drivetrain, perhaps?). I do remember opposite chirality camshafts being advertised.
I can’t easily imagine a modern four cycle engine running backwards spontaneously. As noted above, the valve timing would be awkward.
Are you perhaps talking about “dieseling”? That’s what happens when you turn off the ignition and the engine sputters a few times before finally shutting down. The cause is a hot area in the cylinder causing the fuel charge to ignite even though the spark plug is not operating (functionally the way a diesel engine normally works). A dieseling engine runs in its normal direction, but it feels rough because of the intermittency of the ignition and the low RPMs.
The only time I’ve seen an engine run backwards was with the small two-stroke glow plug engines used in model airplanes. You start those engines by priming them and flipping the propeller. Once in a while, you’ll get a power stroke followed by a dead compression stroke that the engine sort of “bounces” off of backwards, and sometimes the engine will just keep running backwards. It sounds slightly weird, is bad for the engine, and obviously will not propel the airplane in the right direction. I would say it happens maybe once in a hundred starting attempts. The newer electric starters prevent this because they continously drive the crankshaft around in the right direction until it gets going.
I believe I heard once that the old-fashioned hand-crank starters on car engines would occasionally “bounce” backwards and break your arm. Don’t know if this is related to what we are talking about.
I thought so too, but apparently they just put the crankshaft in backwards and mirrored everything else.
Yes, these are the symptoms. Thanks! 
Some diesel truck engines can run backwards if you ‘bounce’ them by letting the clutch out to quickly, but of course diesel engines do not have an ignition system. Since the oil is now being pumped into the oil pan this is a bad thing.