I imagine that with the resulting rearward movement of the CofG, possibly beyond the Centre of Pressure (CP) that the a/c would become extremely unstable, requiring the lightest of touches to alter its attitude, surely it would be virtually uncontrollable by human hand. The usual downward force exerted by the tailplane in S&L would now require an upward force to prevent a nose up. As SD says, with the flaps deployed, the CP will move forwards a bit, but now with no thrust and a shed load of drag. The only good thing is that the stall speed should be lower and glide longer as the tail plane is required to provide some lift too lessing the load on the wing.
Was reading a ILAFFT book on the tube the other day, had a story of a twin whose starboard engine fell off, the specific problemin thise case was that the engine stayed attached via the control and instrument cables but now about six feet aft of the wing!!!! The drag was such that the only way was down at 500fpm. Nothing but forest for miles around, made a successful forces landing in a shallow river!!!! Amazing.