I doubt that there has been extensive (or any real) testing, but if the engine departs the aircraft, I think that we may safely assume that 99% of the time, the CofG will shift so far to the rear that the airplane will be essentially uncontrollable.
I recall a fatal accident in a glider (Libelle, I think) which was being flown solo by a petite woman in the rear seat. The investigation indicated that the ballast in the front cockpit wasn't restrained properly and slipped to the rear cockpit, with the resulting alteration of the CofG being sufficient for a stall spin accident.
Perhaps you are remembering this
Blanik accident? I don't know of any twin-seat Libelles.