This sounds interesting, how would such a method of power generation work?
You may also enjoy: https://www.youtube.com/watch?v=t-O-Qdh7VvQ which is a minutephysics on black hole power using much the same principles but attaining yet higher efficiencies.
PS: Dyson Spheres is misnomer, Olaf Stapledon should be credited for this idea (Star Maker 1937)
Collisions between orbital junk are most likely to happen between objects in the same orbit. And most junk is in some roughly equatorial orbit. So I'd expect the resulting debris to end up in roughly the same orbit, so that the debris would form a sort of fuzzy disk - not a sphere. I wouldn't expect to observe much debris over the North Pole.
The result may not be literally a rigid sphere as people think of it, but if the orbits are packed tightly together enough it'll look plenty "sphere-like" from the next star system over.
A rigid Dyson sphere is probably impossible, and its utility is not entirely clear. Making a Dyson swarm around a star is merely a lot of work, and also has the advantage of immediately paying benefits as soon as the very first satellite is launched.
In modern usage, "damping" usually refers to a drag or parasitic affect in some oscillatory system, but it does not have to be oscillatory. It can be other drag effects that convert energy, with a usual assumption that it will bring the system to a new equilibrium. An object falling through the atmosphere can be considered to have its fall dampened by the air drag, converging towards its terminal velocity.
I am not familiar with all the physics involved in falling towards/into such a star, so I do not know if there are field effects which would cause damping of the fall prior to impact of the trash with an actual surface, similar to the atmospheric descent towards earth. I also wonder if they imagine the orbital system is being damped to allow the trash to impact the star, by bleeding off tangential velocity to decay the orbit.