The second and third episodes of Star Trek: Picard bring us back to the decommissioned Borg Cube we saw briefly teased at the end of Episode 1, "Remembrance." We learn more about the ship--it's a Cube that's only partially active, cut off from the Borg Collective. The Romulan Free State, the government of what's left of the Romulan people, is studying the Cube and slowly pulling it apart.
In Episode 2, "Maps and Legends," and Episode 3, "The End is the Beginning," we get a little more of a sense of what research is being done with the Borg. The people aboard the Cube refer to it as the Artifact, and they both live and work there. Parts of the Artifact are safe, but some are still actively Borg, and it sounds like it's possible to be attacked and even assimilated into the Borg Collective in certain areas of the Cube, if you're not careful. In Episode 3, we also learn that some, including former Borg drone Hugh, are working to reacclimate former Borg drones to life outside of the Collective.
Star Trek: Picard
We don't get much information about exactly what the Romulans are up to on the Artifact, though. Soji mentions the idea that part of the operation is salvaging the Cube and selling what it yields. We also see Soji's work on the Cube with former Borg drones; the Romulans refer to them as "The Nameless," and in Episode 2 we see Romulan doctors removing the former drones' Borg implants. In Episode 3, Soji works with Hugh to try to help Romulan former drones, whose minds have seemingly been badly damaged by their assimilation.
Still, even though we've seen Soji and others helping drones, and other workers hanging around on the Artifact, we don't know what the goal of the work on the Borg Cube actually is. This is the Romulans, after all--the secretive, arrogant, militaristic race that had been in various stages of conflict with the Federation for years. Even though the Romulan Star Empire is gone, thanks to the destruction of Romulus 14 years before Star Trek: Picard begins, it seems unlikely that the new Romulan Free State is just using the Borg Cube to make some cash from salvage, or to make some scientific discoveries.
That viewpoint is bolstered by the fact that Laris explains the Romulans have an aversion to artificial intelligence when she's telling Jean-Luc about the Zhat Vash. If the Romulans aren't fans of synthetic lifeforms, they're definitely going to have some general qualms about the Borg, a race that assimilates other cultures by forcing them to become partially cybernetic. Those feelings might help drive the Romulans to want to free Borg drones from the Collective, like we see in Episode 2, but it seems more likely that they wouldn't want anything to do with a Borg Cube--unless there was some advantage in it.
So what could they be doing? The Borg are a formidable foe thanks to their technology, and they came close to destroying the Federation on more than one occasion. Borg Drones and ships capable of adapting to phaser fire so that it can't harm them, for instance. The Romulans might be hoping to salvage some of that tech in order to bolster their own military capabilities and again become a power in the quadrant. Borg technology could offer a lot of serious advantages to the Romulans, especially if they're still hoping to take on the Federation; the Borg were probably the adversary who came closest to defeating the Federation.
And in Episode 2, we know that the destruction of Romulus didn't wipe out all the old vestiges of militaristic Romulan society. The Tal Shiar, the Romulan Empire's secretive and powerful intelligence agency, still exists and is even operating on Earth. Romulan spies working with the Zhat Vash have infiltrated Starfleet. The Romulans are still formidable, even in their current state and lacking a homeworld. And it seems likely that a lot of Romulans blame the Federation for abandoning them when their planet was destroyed--and are eager for revenge.
The fact is, right now, we just don't know what the Romulans want or what they might be hoping to gain from the Artifact. We know that two former Borg drones from other Star Trek series, Hugh from The Next Generation and Seven of Nine from Voyager, are going to appear on Picard at some point in the future. Given the other elements of artificial life that have been a big part of the story up to now--android clones of Data's technology in Soji and Dahj, the attack on Mars by synthetics, and now the salvage operation on the Artifact--we can expect the Borg to play a big role of some kind as Star Trek: Picard goes forward.
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