In 2368, Enterprise-D encountered a crashed Borg scout ship and recovered a single drone. The drone, later named Hugh was completely cut off from the Borg Collective, and began to develop a sense of individuality. Although the Enterprise crew originally intended to infect Hugh with a virus designed to destroy the Collective, Captain Picard decided that it was wrong to use an individual as a Trojan horse. Instead, he believed that Hugh's newfound individuality would spread through the Collective as a different, yet effective, sort of virus. (TNG episode: "I, Borg")
After Hugh was recovered by the Borg, his individuality spread quickly through his cube, causing the Collective to cut the entire drone population of the cube off from the rest of the Collective. The cube, being populated with incubated drones who had no prior experience as individuals, was lost and confused, and easily manipulated when they encountered Lore soon after. (TNG novel: Greater Than the Sum) The android convinced a large number of drones to follow him in a campaign against the Federation, luring them with the promise of becoming fully synthetic. Hugh, along with a small number of drones, set up a resistance movement, and slowly began to undermine Lore's power. With the assistance of Enterprise, Hugh and his drones managed to defeat Lore's forces. (TNG episode: "Descent")
Forming a Society
After the defeat of Lore, Enterprise left the former drones with various supplies to help them recover, including a sociological database. They chose a rather appropriate name for themselves — the Liberated — and began to build a new society. Instead of directly adopting the culture any of the races in the database, the Liberated began to create new traditions for themselves, including sharing communal meals and a Speaking of the Names, a gathering where the Liberated explained the names they chose for themselves.
The Liberated still had access to Borg technology salvaged from their cube, as well as several ships, including the Liberator. They began to explore the area around their new homeworld, and made contact with several species. Most of their neighbors were frightened at first, and the Liberated decided to begin removing those implants they could in order to lessen their connections with the Borg. In time, the Liberated managed to begin trading with some of their neighbors, while abiding by other races' requests that the Liberated not contact them again. (TNG novel: Greater Than the Sum)
Despite the unity of many of these independent Borg under Hugh's leadership, there were a number of their kind who were dissatisfied with their individuality. Quickly flocking under the leadership of Enab, these Borg became renegades in from their fellow Liberated in 2371 and sought a means to return to the hive mind. Capturing the Klingon vessel Taj, they began to attack the Tholian Assembly in order to study the Tholians' natural hive mind. Their actions led to increasing hostilities between the Federation, Klingon Empire and the Tholian Assembly which nearly erupted in war. However, the crew of the Enterprise-D managed to learn of Enab's actions and stopped him from his continuing his campaign. (TNG comic: "Cry Havoc")
New Problems, New Opportunities
However, their peace was short-lived. Less than four years after the Liberated were freed, they came under attack from two fronts. In 2373, the Borg invaded a realm known as fluidic space and attempted to assimilate Species 8472. Species 8472 proved resistant to assimilation, and began an invasion of Borg space. Their efforts were not limited to the Borg's home territory, the Delta Quadrant, but included all outlying Borg areas, including the Liberated's territory. Since Species 8472's biological attacks quickly spread through the highly centralized Borg systems, the Liberated retrofitted their remaining vessels with decentralized technology, including individual computer cores and warp drives.
Unfortunately, this attracted the attention of the Borg. In addition to the new possibilities of the decentralized systems in fighting Species 8472, the Borg began efforts to re-assimilate their lost drones to bolster their devastated numbers. Even after Voyager managed to force Species 8472 back into fluidic space, the Borg did not cease their attempts to recapture the Liberated. It was only due to their individual ingenuity with modifying Borg technology (and, presumably, technology introduced by Lore) that the Liberated avoided re-assimilation. (VOY episode: "Scorpion"; TNG novel: Greater Than the Sum)
The fight against the Borg was made easier in early 2376, when Voyager freed all of the drones who possessed the ability to enter Unimatrix Zero. The Zeros, as the Liberated called them, were able to weaken and distract the Borg from their fight against the Liberated. Some Zeros, including former Enterprise crewman Rebekah Grabowski, were close enough to the Liberated to bring more people and ships to the fight. (VOY episode: "Unimatrix Zero"; TNG novel: Greater Than the Sum)
To the Liberated, the Zeros represented both an opportunity and a threat. Some Liberated believed that the culture and traditions brought to them by the Zeros would overwhelm the culture they had striven to create since their freedom. Other Liberated, including Hugh, believed that the Liberated culture was dynamic enough to adapt and adopt aspects of the cultures represented by the Zeros.
However, the Liberated could not simply ignore the help the Zeros offered. With the assistance of several groups of Zeros throughout the galaxy, the Liberated managed to make multiple successful attacks against the Borg. Even after Voyager managed to destroy the Borg's transwarp network, the Liberated and the Zeros in their sector continued the fight. They managed to destroy the Queen being created in their sector of the galaxy, though it came at a high cost to the Liberated. (VOY episode: "Endgame"; TNG novel: Greater Than the Sum)
But even in light of their victories against the Borg, the Liberated remained fractured. They realized that there was one major aspect of themselves that set them apart from other races - the ability to procreate. The Borg had ripped this ability out of all of their drones - both incubated and assimilated - and the Liberated had no way to reproduce and grow as a result, except by liberating other drones. (TNG novel: Greater Than the Sum)
The Einstein Incident
Although they had made major strides on their own, it took an outside force to move the Liberated forward, and once again, it involved the crew of the Enterprise.
In 2380, the Borg assimilated the Starfleet vessel Einstein, which set course for the Delta Quadrant. Einstein eventually came across the USS Rhea, exploring the star cluster NGC 6281 entity, which was later discovered to be one single entity spanning several light-years. The entity could not bear to see a loss of life, and so it froze the half-assimilated Rhea in time while sending Einstein to the closest Borg world it could locate via quantum slipstream - the Liberated homeworld. The Liberated were able to fight off the Borg vessel, and though they were in no way connected with these Borg, they could sense that Einstein planned to return to the entity and assimilate its knowledge. Hugh and Gradowski immediately set out on the Liberator to beat Einstein to the cluster.
Once Liberator arrived at the cluster, it made contact with a new Enterprise, commanded by Captain Picard, the same man who had allowed Hugh to spread his individuality to the Borg twelve years earlier. The Liberator offered assistance in defeating Einstein, and also requested Enterprise's assistance in giving the Liberated the ability to reproduce. Although the ensuing battle resulted in Hugh's self-sacrifice to destroy Einstein, enough of his genetic material was saved to allow Grabowski to bear their child, giving the Liberated the opportunity to become a true race unto themselves. (TNG novel: Greater Than the Sum)
Behind the Scenes
In Star Trek Online, lifetime subscribers are able to get a new playable race class known as Liberated Borg which is available to both Federation as well as Klingon Empire players. They gain four additional traits including Borg Nanites, Efficient and Borg Neural Blast.