Fighter jets like PAK-FA ,F-22 , Su-35 etc are designed to be so inherently unstable that a human can't fly one unassisted
The best description I have read is imagine you are sitting on the bonnet of a car (sorry, for those Americans I mean the hood). You have in your hands the handle bars of a bicycle which is facing backwards... its rear wheel is to the front and the front wheel is right in front of you.
Now imagine the car starts moving... you have to steer the bicycle with lots of tiny movements every second to keep it going backwards... the faster you go the more precise the movements... few people could keep the bike under control at more than a few kms per hour.
BTW add the F-16 and F-117 to the list of unstable fighters.
As a hint when a fighter is landing or taking off look at the horizontal tail... if it is making lots of oscillations in pitch rapidly then it is likely an unstable design... without control it would try to fly tail first.
Aircraft that are stable need to overcome the inertia of their stability before they can start to turn or roll or manouver... a very short delay but a delay nonetheless.
A pilot would not be able to land these aircraft if the fly-by-wire systems became inoperative .
Most unstable aircraft have quad redundant fly by wire systems that are independent any of which would be sufficient to keep the aircraft in flight. The backup systems might not allow fantastic flight performance but would ensure flight stability to return to base and land.
Stability refers to the relative positions of the center of lift (cl) and center of gravity, (cg). When the cg is ahead of the cl (stable) an aircraft that stalls can fall forward, increasing speed and recovering.
Both Cg and cl change in flight depending on speed and altitude.
Unstable aircraft want to fly tail first.
MiG-8 was the first aircraft that was technically stall proof... very simply if you take a plane like a MiG-29 when the main wing stalls the tail surfaces have likely already stalled and the sudden loss of lift means the nose will pitch up. the sudden pitch up increases drag which reduces airspeed... eventually the main wing will stall and the plane will likely go into a serious stall usually falling to the left or right rolling over out of control.
The MiG-8 had a swept wing and canard foreplanes. When the foreplanes stalled the nose dropped down which increased speed and lowered the angle of attack for the main wing and automatically recovered from the stall.
The only problem was that you did descend a bit so you had to have altitude.