A good portion of aircraft, especially those designed before the 1970's, possessed static stability. However, modern fighters (and some airliners) have been build with relaxed static stability.
This question was aroused by the book Designed for the Kill by Mike Spick. On page 119, it states (in reference to the Shenyang J-8 II Finback B):
In 1991 improvements were stated to be in hand to improve subsonic manoeuvrability, and one of the obvious moves would be to introduce variable camber by using leading edge slats. There can be no doubt that FBW and relaxed stability would also benefit it considerably, while weight reduction could be achieved by the use of composites.
How would a fighter such as the J-8 physically be changed to change the centre of gravity in relation to the centre of lift? Would the wings be resized/moved? Would the tailplane be made smaller? Would internal items be shuffled around to put heavier ones at the back? Or could some sort of clever aerodynamic device be added to modify the airflow somewhere?