FBW makes all sorts of weird stuff possible.
Computer controlled fly by wire does....
Actually, not so much. The "relaxed" stability margins that 4th and 5th generation fighters fly with are just that: relaxed
margins. Ditto for aft CG fuel loading of airliners at initial cruise to reduce trim drag.
In an effort to work with more efficient configurations, aft CG, transonic and supersonic flight, and higher maneuverability vs. stable CG and dynamic stability, commercial and military design has progressed to the point of reducing margins below the ability of the pilot's ability to maintain control in dynamic, not static flight modes. Please refer to the Cooper-Harper scale and its influence and implications on controllability.
"Relaxed stability" or dealing with dynamic instability has been done for over 60 years. First with analog SAS (stability augmentation system), later with digital. All successful, operational FBW air vehicles are statically stable and may venture into dynamic instability in parts of the envelope. All of them will depart computer-controlled flight as the stability limits are reached.
("Envelope": defined as the dynamic pressure/Mach/alpha/pitch-yaw-roll-rate/CG vs. altitude that an aircraft is capable of achieving)
No successful program has ever flown a vehicle with a wide operating envelope that was statically unstable in level flight.
Read that 2, 4, 10 times and do the research before responding.