did they defeat the borg ?

Not permanetly no, but the Borg did suffer a heavy defeat thanks to Janeway.

You might enjoy reading this! http://en.memory-alpha.org/wiki/Borg

will do

History Edit

A Borg skeleton on a ruined planet

The precise origins of the Borg are unclear. As of 1484, they were reported as controlling only a handful of systems in the Delta Quadrant, but by 2373, they had assimilated thousands of worlds. In addition to this stronghold in the Delta Quadrant, the Borg also dispatched vessels throughout the galaxy via transwarp conduits. (VOY: "Dragon's Teeth", "Scorpion", "Endgame")

A Borg vessel traveled back in time from 2373 in an unsuccessful attack on Earth in 2063. (Star Trek: First Contact) Drones which survived this defeat were discovered and reactivated by Human scientists in 2153, and transmitted a subspace message to Borg space before being destroyed by the Enterprise NX-01. (ENT: "Regeneration")

In 2293, the Federation offered aid to El Aurian refugees fleeing the Borg. (Star Trek Generations) However, each of these incidents contributed almost nothing to the Alpha Quadrant's awareness or understanding of the Borg Collective.

By the 2350s, rumors of an alien race called "The Borg" had reached the Alpha Quadrant, inspiring exobiologists Magnus and Erin Hansen to set out in search of them. Their research took them all the way to the Delta Quadrant before they and their daughter Annika were assimilated in 2356. (VOY: "The Gift", "The Raven", "Dark Frontier") Borg activity in the Alpha Quadrant, including the assimilation of the USS Tombaugh in 2362 and assimilation of outposts along the Romulan Neutral Zone in 2364, were complete mysteries to Starfleet. (VOY: "Infinite Regress"; TNG: "The Neutral Zone") The Collective's true nature was finally revealed to the Federation in 2365 when Q took the USS Enterprise-D to meet a Borg cube near the J-25 system. (TNG: "Q Who")

In late 2366, a Borg cube invaded Federation space and assimilated Jean-Luc Picard, whose tactical information contributed, along with the Borg's own vastly superior power, to Starfleet's disastrously one-sided engagement with the cube, the Battle of Wolf 359. A fleet of forty starships assembled to combat the cube. All but one of these ships were destroyed, while the cube remained intact, damaged but healing rapidly. The Enterprise-D recovered Picard and used his connection to the hive-mind to disable the cube before it could attack Earth. (TNG: "The Best of Both Worlds", "The Best of Both Worlds, Part II")

During the 2370s, the Borg were beset by several major setbacks in the Delta Quadrant, all witnessed by the crew of the USS Voyager.

The Borg-Species 8472 War decimated the Collective from 2373-2374. Voyager's liberation of Seven of Nine allowed Unimatrix Zero to create an active resistance movement in 2377.

In 2378, a crippling blow was delivered to the Borg when Voyager discovered one of their transwarp hubs and destroyed it, killing the Borg Queen (again) and devastating the Unicomplex in the process. During this battle, the Borg were infected with a neurolytic pathogen, which was carried by Admiral Janeway and designed to disrupt the hive mind, to bring chaos to order. It was this pathogen that killed the Borg Queen, and allowed Voyager to destroy the transwarp hub. (VOY: "Scorpion", "Unimatrix Zero", "Endgame")

as you said svanya

they havent been completely destroyed

here is an alternate outcome from thsame sit svanya posted

Parallel universes Edit

In one alternate quantum reality, Captain Jean-Luc Picard was lost in the Battle of Wolf 359 and William T. Riker succeeded him as the captain of the Enterprise-D with Worf as his first officer.

In another alternate quantum reality, the Borg emerged victorious from Wolf 359 and successfully conquered the Federation. A battered Enterprise-D which was likewise under Riker's command was one of the few remaining Starfleet ships by 2370. That reality's Riker was desperate not to return to his universe once all of the Enterprises began spilling into a single universe from a quantum fissure. After attempting to get the attention of the present reality's Enterprise by firing lightly upon them, the ship was accidentally destroyed, when its shields collapsed, presumably due to damage accumulated from fighting the Borg. (TNG: "Parallels")

so 2 possible outcomes however i think it is generally that they the borg wa beaten back and it doesnt seem if there was any other. with regards to that.

"any other outcomes with regards to that"