I imagine it's much easier to control on the trade side of things if governments really want to. Fish have to be brought relatively fresh to markets where there is demand.
Depending on the species. There are factory ships, such as the name suggest have onboard factories that process the fish into filets, pack, freeze and stow the fish, enabling the vessels to stay longer out at sea - limited either by their cargo capacity or quota. Arguably this is good for the quality of the fish as well since it is frozen fresh.