Earlier quoted context omitted.
It's not the popular papers that are important. Those will be well spread already. It's the unpopular "rare" ones that need help. You mean the libgen torrents or is there something spefically branded sci-hub?
It's possible to solve, you just make users download a zip file which includes 10 papers including the one they're interested.
It would probably be better to break down the torrents into smaller, more coherent, and organized collections that contain all associated metadata (e.g. a collection of biology papers from a certain time-span or set of publications). That way you might incentivize people to maintain smaller personal-use archives that could be recombined back into the whole, if the need arises.
You could perhaps even build a system that could automatically generate, publish, and consume torrents with a particular (metadata + content) layout, but that's not restricted to a particular set of torrents. Then it could just consume certain topics from a feed of new torrents, from various sources, on the Pirate Bay.