Canonically speaking, the chronology of the "prime" timeline of the Star Trek universe ends either with Star Trek: Nemesis, or perhaps with the destruction of Romulus by the Hobus Supernova in Star Trek (2009). Both of these are set after the return of Voyager.
Since neither of these stories mention the Borg at all, that I can recall, the only possible answer is: No. There is no canonical information on what happened to the Borg after "Endgame".
Pocket's novels set after the end of the series provide one possible answer (including a fairly epic crossover between TNG, VGR, and DS9 casts). This arc eventually resolves both the origin and the fate of the Borg, once and for all. It's important to remember, however, that the Star Trek EU has never been remotely canon, and future writers both of novels[*] and of possible movies and television series are free to ignore them entirely.
Star Trek: Online has a different, quite contradictory, possible answer which preserves the Borg as a threat (albeit a very different and evolving one) well into the 2400s. STO, however, is also not canon.
At this writing, there are no known plans to extend the "prime" timeline further forward in a canon medium (that is, television series or movie produced by Paramount). It is therefore very likely that no canonical answer will ever be known.
[*] Pocket has been making some effort in recent years to harmonize continuity within their novels--efforts that used to be actively stymied by Paramount's monitors and now seem to be permitted on the understanding that nothing Pocket does is binding on Paramount.
In early 2020, Star Trek: Picard finally extended the canonical timeline as far as the year 2399, 14 years after the supernova that destroyed the Romulan homeworlds. While this series did include, as one of its locations, a "broken" Borg cube known as The Artifact, we still have little additional information about what happened to the Borg as a whole.
We do know that the Borg were still an active threat as late as the 2380s, and that this particular cube attempted to assimilate a ship that was carrying Tal Shiar agents, including at least some Zhat Vash initiates. As a result of assimilating the Zhat Vash in particular, and coming into contact with The Admonition, that cube basically suffered the Borg equivalent of colony collapse disorder, allowing the Romulans to capture it.
Since then, the Romulans have mined the cube for technological secrets, while a Reclamation Project led by Hugh (formerly Third of Five) attempted to de-assimilate the former members of that cube's collective, with some success.
The fate and activities of the Borg Collective, beyond that one cube, are still unknown.