Maybe not hunting nets per say, maybe just a huge trawling net, or some sort of trawling-foam since we're in space. As high velocity objects begin to hit it, the foam will gain speed, but overtime, with presumably random speed-object collisions, the foam and its captured contents should have their speed reduced to 0 and fall. Doesn't need to be in foam or net form, but it does need to be a massive-entanglement-object, or MEO for short.
I'm probably under thinking this, but wouldn't the overall momentum of the debris be conserved so you'd have a bias in debris velocity in whatever direction the original objects were orbiting (presumably not random)?
I would assume that as the debris cloud became more biased in one direction, it would be more and more likely to encounter new debris coming in a different direction.
At least at geosynchronous altitude it seems like it would be significantly biased in the direction of Earth's rotation, especially along geostationary orbit.