(covers information from several alternate timelines)
Unimatrix Zero was a virtual construct and resistance movement created by a group of Borg drones. After it was shut down, drones formerly connected to Unimatrix Zero continued to oppose the Borg Collective in the Borg Civil War.
This construct was created by Borg who had a recessive genetic mutation which gave them the capability to create this virtual world and to live in it, free from the hive mind as individuals, while regenerating in their alcoves. Individual Borg were connected to Unimatrix Zero via their interlink frequency, based on a tri-axillating modulation. This modulation made sure that not even the Borg Queen could disrupt their link.
How Unimatrix Zero came into existence was unclear. Some believed it started with a random malfunction during the assimilation of a single drone which eventually spread to other drones. The genetic mutation was rare and only one in a million drones possessed it, whether or not they were adults or children, still in a maturation chamber.
Although this mutation made it possible for a drone to live in Unimatrix Zero, they only were aware of it as long as they were in it. When a drone's regenerative cycle ended it could not remember the experiences gained while serving the Borg Collective. Entering Unimatrix Zero was only possible when a drone entered its regenerative cycle. For non-Borg entering was only possible via a mind meld with a drone in its regenerative cycle. The number of Borg drones who made up Unimatrix Zero were estimated to be about twelve thousand or more.
In Unimatrix Zero a drone could opt to assume the appearance it had exhibited before assimilation into the Collective, and most choose to do so. A drone was aware when its regenerative cycle would end, giving it the opportunity to say goodbye to others before exiting to serve the Collective. Once inside the Unimatrix a drone could call another drone in its regenerative cycle. Only drones who possessed the genetic mutation could be called to and enter the Unimatrix, which served to let them regain some part of the lives and individuality they had prior to assimilation.
Although a drone could be killed within Unimatrix Zero, he or she would enter it again during the next regenerative cycle.
Unimatrix Zero was undetected by the Borg Collective until 2376. In this year the Borg Queen found their interlink frequency. Although the Collective could detect the drones with the genetic mutation, which they saw as an illness, their method was slow and would take centuries to find every drone with the mutation. By examining the cortical array of drones with the genetic mutation the Queen found their interlink carrier band, which she was able to use to send Borg drones to Unimatrix Zero in order to attack its occupants.
In the following year Axum, one of the drones with the mutation, called Seven of Nine back into Unimatrix Zero to help them fight the Borg. A nanovirus was devised by them which would mask the biochemical signature of the genetic mutation, making it impossible for the Borg to detect them. But they could not introduce the virus into the Collective without Seven's help; as the only member of Unimatrix Zero not part of the Collective, Seven was the only one who could retain the memory of Unimatrix Zero when she wasn't regenerating.
Seven of Nine, being a member of Unimatrix Zero for almost eighteen years, asked Captain Kathryn Janeway for help. It was Janeway who suggested to Axum to begin a resistance movement to undermine the Borg's control over them once their mutation could no longer be detected.
After Janeway agreed to help, the nanovirus Axum designed was modified by the The Doctor so it would also nullify the cortical inhibitor, so drones with the mutation would keep their memories about Unimatrix Zero while being part of the Collective.
Inside Unimatrix Zero, drones sent by the Borg Queen were being fought.
Although the Borg Queen warned Janeway not to interfere – and even tempted her with an offer to send the USS Voyager back to Earth – Janeway went through with her plan and, after allowing herself, Tuvok and B'Elanna Torres to be partially assimilated, succeeded in infiltrating the central plexus of a Borg cube and releasing the nanovirus.
After the nanovirus was released, the Borg Queen began to lose contact with drones possessing the genetic mutation. In an attempt to force Captain Janeway to give her an antidote for the nanovirus, the Queen interrogated her and destroyed entire Borg vessels in which she could no longer hear only two or three drones. Despite this, Janeway still refused.
The Borg managed to reprogram the nanovirus to shutdown the autonomic functions of the drones with the genetic mutation, making them die within minutes. The Queen herself would release it from within Unimatrix Zero. When Janeway was told by the Queen she had to make a decision, make the drones return to the Collective or they would be killed, she conferred with her First Officer Commander Chakotay via Voyager's holographic system and told him Unimatrix Zero could no longer exist.
To save the drones with the genetic mutation it was necessary to destroy Unimatrix Zero. This was done by the Voyager and a Borg sphere under the command of the Klingon Korok, an occupant of Unimatrix Zero. Both starships had reconfigured their deflector emitters to disrupt the interlink frequency and so destroyed Unimatrix Zero.
Although this resulted in the destruction of Unimatrix Zero, it also resulted in the creation of a 'fleet' of multiple Borg vessels under the control of former drones, these drones going on to make up the resistance movement against the Borg; Unimatrix Zero was gone, but the drones themselves had survived. It is unknown if any of those drones did succeed, although Korok promised to stay in contact with the Voyager. (VOY: "Unimatrix Zero", "Unimatrix Zero, Part II")