A good is excludable if people can be prevented from using it. If one person is using any rival good then this good won't be available for others. You asked about rival and non-excludable good such as Common-pool resources. Examples of Common-pool resources is fisheries, forests, groundwater basins, oil fields and so on. Unlike pure public goods, common pool resources face the problem of overuse (the tragedy of commons).
Let's see the case of fisheries you talked about. Generally, fishermen are free to fish in the sea. The tragedy of the commons problem tells us that each of the fishermen will try to catch more fishes as they are rival goods, unlike public goods. Therefore, this common pool resource of sea-fishes will be vulnerable to get extinct or get empty due to overuse. To reduce the chances of this happening, government or any common group will be given authority to manage it and reduce the overuse of it. Nobel prize winner economist, Elinor Ostrom noticed this and talked about collective-choice arrangements and effective monitoring of common pool resources.
Coming to your doubt, CPRs may or may not be sold. Talking about Sand in the river basin (another example of CPR) there is an example of selling of rights to mine or excavate sand. Also, there is a prohibition of fish mining from the area where fishes are endangered species. due to over mining or preserving the bio-diversity.
Therefore, it depends on the situation whether Common pool resources can be sold or not.