My record is a foamy RC flying wing that flew itself for 10 minutes without any input.
All REAL fighter jets are unstable. Stuff you do from foam may or may not be stable, it is irrelevant here.
Stability is not necessarily a friend. In fact,
stability is the enemy of agility.
Imagine the situation like a book sticking out the edge of the table. If you tilt the book outward by a certain amount (angle), it will fall off the table. But if you tilt the book just a little but below that "fall off the table" angle, it will just fall back to its initial state. That there is
a force to brings it back to the initial state is what makes it stable. When the book's CG is very near the edge of the table, the "fall off the table" angle is very small. Add just a little energy (ie: tilt the book just a bit) and off it goes dropping to the ground.
So, stability describes an energy to keep it at current state. On an airplane, to make a turn or a slow dive, you need to overcome (over-power) the energy that keeps it stable so you can change state. The more stable, the more energy it takes to break the stability, the more energy, the more time it takes to add that energy. So it will take more time to turn, rotate, dive -- ie: less agile.
In fact, even more extreme than flying wing, stuff like forward sweep wing is of interest is because it is inherently unstable and thus inherently more agile.