I think you are talking about the canards. Canard aircraft are much more common than you think and are certainly stable. For example, see this Rutan VariEze:
Image from airliners.net
(Static) stability means that the aircraft will return to its original position after a disturbance. For longitudinal stability (i.e. about the pitch axis), if some disturbance causes the aircraft angle of attack to increase, it should return t its original (lower) angle of attack by itself.
In case of the canard aircraft, the center of gravity is forward of the main wing.
Image from f-16.net
In this case, it is the main wing which is stabilizing. If for some reason, the angle of attack increases, the canard produces a moment about the c.g. that tends to increase the AoA. However, the wing also produces more lift (as AoA is higher), and this results in a stabilizing moment about the c.g.
The aircraft may still (most probably) remain a dream for various reasons, though I doubt having a canard has anything to do with it (Actually, the span is on the larger side). Without details, its just speculation.
Interestingly, the aircraft looks similar to the Rutan Voyager, which holds the world endurance record and had problems with pitch stability.
Image from nasa.gov