There have been recent reports in the news of a blue whale, towing behind it a huge morass of driftnet wrapped around its tail. It does not take much googling to read about the destructiveness of lost nets, which float along, tangling things up and killing them like some montrous immortal jellyfish.
propose that driftnets be fitted with special lead spheres. These spheres would be neutrally buoyant, filled with air. They are sealed by something which degrades after a certain amount of contact with water - perhaps some polymer, or maybe leather or some wax which marine organisms would eat. When the seal is broken, the weight fills up and becomes heavy.
Nets in use would not be much more difficult to use with the weights on (although they would be heavier out of the water). Fishermen who noted that a weight had flooded could turn it it for a free fresh one. But when the net was lost, after a period of months all the weights would flood, and the net would sink down the the bottom, relatively out of harms way.
I could have sworn [Worldengineer] had a driftnet idea also, but I couldn't find it. Link it up, [W].