The more forward the tips of a bow are in relation to a riser, the more prone the bow is to twist during an attempt to string it. Meaning, if you compare two bows that are otherwise identical but one with the tips 3" in front of the riser and the other is 1" in front of the riser, the one that is 3" forward is more prone to twist on you because small variations off an in line pull will result in a force that is a greater distance out of alignment. If you have two parallel lines that are so close together that they appear to be the same line...but one then changes angle at a given "X" degree...the further you continue down that line the greater the distance one travels away from other line that remained straight (the initial plane). It is just physics. The further one travels off line (such as by bow torque during stringing at "X" degree), the more the radical limb is pulled out of alignment.
Additionally, the harder/more radical the curve, the more prone it is to twist. Meaning if you have two bows with the same amount of backset (lets say 2"), but one has the reflex is spread out over a full working limb while the other is static (radically recurved at the tip), the one with the greater "hinge" is more prone to twist. Imagine taking a wire and bending it to a V. If you were to rest the V on a string, it would turn upside down and self-center (become stable) by taking a deflexed shape. If you insist that it stay upright (reflexed) and balanced on the point at the bottom of the V, it would remain unstable and be more prone to twist by being hyper sensitive to any out of alignment pull that is out of alignment with the fulcrum. Again, it is just physics.
Now, all that said, one can indeed make a static bow that is sufficiently stable for shooting if the braced position is one with the tips having enough "string follow" to maintain a desire to pull in alignment...but it is certainly a tricky balance. The tips should NOT still be pointing forward when the bow is at full draw. IMO, the tips should go "vertical" around mid-draw in order to maintain stability of a static bow. If I am right (as this is just MY OPINION), this means the tip angle at full draw would be off vertical by about the same amount as they are at brace height, but of course in the opposite direction by pointing rearward instead of forward. Too MUCH string follow at full draw and you loose the benefits of the static design as string angle will be increased and might as well go with a full working recurve. Too LITTLE string follow at full draw (by string follow I am referring to the degree of pointing rearward), and you give up too much stability. Now, that said, the goal of a static is NOT just about string angle at the tip. The goal is to get the limb to work closer to the fadeouts without adding mass to the tips. This increases stored energy. A very short limb after a hard curve doesn't really add much energy to the fadeouts as there isn't enough leverage there (proportion of the limb) to drive the energy into the fadeouts...but it is also MY OPINION that one of the best ways to make a static bow HYPER SENSITIVE is to have too much limb length AFTER the hard curve. A long lever (limb) after a hard sharp curve makes the bow too easy to torque during draw. The harder/more radical the curve, the shorter the limb should be out past the curve...but if you go too short it doesn't provide any leverage (not good). Again, you have to balance curve and limb leverage to balance energy and stability. I like Sixby's design because IMO it appears near optimal for a static design. While he does have enough limb after to the curve to improve the stored energy to his limb's profile, it also appears that when given the choice between stability vs energy, he chose to error on the side of stability by not making the limb too long after the curve...therefore minimizing the instability issues of a static limb design.
Now, that said, I have never seen a static design being used in Olympic competition. Of course, in the Olympics, noise isn't an issue so the static's benefit in the noise department isn't considered an advantage as it would be in bowhunting. But, I do believe a bowyer can get much of the speed/energy the static has to offer in a full working recurve IF the design is good that also has the tips go vertical around mid-draw, as this would minimize string angle at full draw (within reason) while ALSO maintaining stability (that is obtained string follow during the draw). It is all about BALANCING the traits we desire in a way that produces an optimal bow for our needs.
Unbraced profile alters stability during stringing and also influences initial stored energy at brace.
Braced profile alters stability during shooting and also influences stored energy throughout the draw.
Now that said, STABILITY and ENERGY are very much, but not entirely, in opposition with one another when it comes to bow design.
On stability - The most stable design is a straight limb. This of course is also the least efficient, with the exception of an entirely deflexed/string follow bow being even less efficient than the straight limbed bow (although in my opinion the string follow bow is NO MORE stable than a straight bow as a straight bow and a string follow bow with both have the same strung profile...and it is the strung profile that ultimately determines stability for shooting).
On energy - The more ENERGETIC design is reflexed. We can add reflex to a bow, but doing so typically results in a loss of stability unless one also adds deflex. A good bowyer CAN add more reflex than deflex to create backset without causing a significant loss of stability, but only if they know how to balance these attributes well. If it isn't done right, the bow will be sensitive.
Both static and full working can be good and/or bad. This is left up to the skills and knowledge of the bowyer...as a good bowyer knows how to BALANCE these traits in a manner that results in good shootability.
Deflexing the riser, or shortening the riser to get the bow to work closer to the hand will add a degree of string follow closer to the fulcrum (the bow hand). Too much of this though, and you loose efficiency by having too much mass movement (limb movement) that results in an absorption of energy.
These situations all go back to..."Just because a little is good doesn't mean a lot is better." It is all about balance.