I always envisioned a sort of huge, sticky balloon. You launch it, and it inflates into a large sphere, covered with balloonlets that each support a pad of debris capture material. It would look like a huge raspberry.

When enough of the balloonlets are destroyed by collisions, you de-orbit the thing.

Obviously, a lot depends on the as-yet-unknown debris capture material. It would have to be very elastic, sticky, and UV-resistant.

If the capture material is sort of a slimy foam that can expand greatly in volume without losing cohesiveness, the inflatable support structure might not even be necessary. You launch the mother slime, then add the foaming agent in orbit. Anything that hits it either sticks to it or slows down while passing through, without generating additional debris.