Bacteria!

Nothing, not even the Borg could ever totally eradicate bacteria within an active biosphere (or should I say biocube in this case!).

Short of tossing the Borg-Cube (or even the entire planet Earth) into the sun or a black hole, or in front of a supernova, bacteria is there to stay permanently within any active biosphere.

And if the biosphere exists long enough, then bacteria will adapt (adapting even to the adaptions of the Borg), and will eventually begin evolving into something else, and eventually likely transform the biosphere in some fundamental way.

On Earth, that took 2 to 3 billion years for bacteria to accomplish. Eventually involving the evolution of bacteria into plankton early in the process, and then the subsequent utter transformation of the entire planetary atmosphere from one of mostly Nitrogen/CO2 to one of mostly Nitrogen/Oxygen (killing off so many of Earth's original species in the process to which oxygen was a highly volatile and potent toxic atmospheric pollutant).

On a Borg cube which is much more responsively self aware and self regulating... maybe it would take a few billion years longer perhaps?

But no worries: such timelines are no worry for bacteria: they're very patient, and utterly resilient, as they proved here in Earth's evolutionary history.

Ultimately the Borg ain't got nothing on them! Bacteria and the initial microorganisms they will evolve into, are the original hyper-adaptive lifeform!