Rather than thinking of tendencies to do this and that (yes, I know, that's how pilot training has addressed it for donkey's years .. but it is done, generally, in an inappropriate way, unfortunately) .. a better (and conceptually simpler) way of looking at (longitudinal) static stability (usually abbreviated LSS) is to consider stick forces .. which is how the thing is measured.
Starting from a trimmed speed (and without any retrimming), static stability requires that,
(a) to fly at a lower speed (doesn't matter how that state is achieved), and maintain that lower speed, requires a
pull force on the stick
(b) to fly at a higher speed, and maintain that higher speed, requires a
push force on the stick
The magnitude of the force as the speed delta varies (ie the slope of the speed against force curve) is a measure of the magnitude of the stability.
If the force gradient gets too shallow (static stability gets too low) the aircraft becomes too twitchy to fly reasonably and at risk of structural damage due to pilot mishandling .. hence one of the reasons for CG envelope limits.
If the force gradient reverses (ie pull becomes push and push becomes pull) the aircraft piloting workload becomes extremely high (the technique to fly it is quite different to normal flying) and, as a good bet, only folks with a flight test background are likely to be able to recognise and use the relevant techniques within the short timeframe available to get/keep things under control (typically after liftoff with a misloaded aircraft .. ie excessive aft CG)
If the aircraft is dynamically unstable, either you have a means of stepping out or you, very likely, die. Certainly, unless your aircraft has some fancy electronics in the control system, it is not flyable by a Mk. 1 pilot.
For those interested, some words of wisdom can be found at
AC 23-8C p78 and subs