Also the CoG would be altered, the plane would fly all squirrelly, and any use of the remaining stab+elevator would include a rolling motion (just like a rudder).
The CG would shift slightly forward, though, not back. Planes that are designed to be more maneuverable/less stable generally have their CG further back than planes that are designed to be more stable/less maneuverable. There's a trade-off involved; less stable is more maneuverable. More stable is less maneuverable. So, a slight shift forward could actually make the plane
less "squirley".
The required CoG of a plane isn't a precise point, it's more of a "range". Flight testing will reveal the "best" point within that range, but there's some allowable shift forward and backward from that point. Things like cargo, fuel, or passengers, will shift the actual CoG forward or backwards. If the fuel or cargo (ordinance) are moved, or burned, or "dropped", the CoG will change (along with the current wing-loading), if that weight was initially placed anywhere forward or rearward of the CoG. Shifting it forward (as long as the forward limit isn't surpassed) will make the plane more difficult/slower to re-direct (which is also what we generally consider to be more "stable"), shifting the CoG rearward makes the plane easier/quicker to re-direct, until it reaches a point where it's too "squirly" to control (less stable).
That rolling movement you mention is present in AH from what I've seen.
I'm not arguing that a damaged plane should be more stable, just that a slight forward shift of the CoG shouldn't be a deal-breaker.
