Would you really need a net that captured the debris? How 'bout a large balloon full of foam, like the insulation you can spray in crevices in your house. A bolt hits the balloon and passes through, but it loses enough velocity that its orbit decays and it burns up in the atmosphere.
Once enough objects hit the balloon that it’s in danger of breaking up, it deorbits and burns up.
If all goes bad up there, things will self clear from the bottom up (and the top down) and it won’t be long before the lowest usable orbit is safe ‘enough’ again. Yes it will require more boosting but it can be used if we had to.
What about the debris from the foam? Each object passing through the balloon will create multiple pieces of foam debris, themselves becoming hazards for objects in orbit. To be able to slow down the debris that passes through the balloon, the foam itself would have to be pretty “stiff”.
Designing the foam so that it degrades over time in sunlight might help, but that just changes the size of the foam particles from pebble-sized to sand-sized.
Hopefully a formulation can be found that’s sufficiently sticky; it would either adhere to the mass of foam in the balloon, or to the piece of debris that passed through it.