The system could be entirely passive, just letting orbital mechanics sweep up a given orbit, but you could go further. A foam could be chosen such that a ground based laser could ablate some of the material which would work like a rocket thruster, allowing the foam block to be maneuvered and prolonging its time in orbit if desired. The ground based laser (or perhaps an array of such lasers for more flexibility) would need to be powerful, but since it doesn't need to go into space the construction, operation, and maintenance costs can be relatively low and it can be reused for many years.
The main challenge of such a proposal is that the foam must be carefully chosen such that both impacts, radiation, and thermal cycling don't cause it to deteriorate and break up into smaller pieces, as this would be simply adding to the debris problem. Another challenge will be getting the foam to deploy reliably in the correct shape. One of the more interesting solutions to both problems is to actually use a foam which is cured by solar UV radiation, so the canister releases a fluid that forms a sphere due to fluid forces and only the surface is completely solid. As the surface gets damaged by impacts, newly exposed interior material fills in gaps and then crosslinks as it is exposed to UV light, healing the damage.
