Longer links will allow the sway bar to rest in a normal position. As the truck gets lifted, the sway bar's core gets further from the link's mounting points, rotating the "arms" that reach out from the core (mounted on the axle), up to the links. These arms are designed with a specific angle in mind... shortening them or lengthening them (via rotating the bar) changes the force applied to the sway bar, and probably the angle the force is applied as well.
So several things can happen... shortening the arms would increase the tension/compression in the end links (same weight of truck but shorter lever), causing the links to break. changing the angle of the force application to the bar can cause the bar to break off because the bar bends during articulation rather than twists, as its supposed to.
Yeah, one would generally want to keep the bar as it was designed to work. So lifting up a bunch, longer links would be ideal if you want the sways to work properly and not rip stuff up. I've seen a bunch of threads about broken sway bars and that longer links fixed the problem.
Adjustable links and adjustable bars are slightly different thing... they let you tune the aforementioned lever arm length to get different ride characteristics. But it's the same idea I suppose.