System J-356 was a star system located in the Delta Quadrant, and by 2377 was under the control of the Borg.
The Federation 3rd Fleet was in the area searching for the Borg Staging Grounds when they were attacked by a number of unknown ships. The USS Allegheny was the sole survivor of the attack. The Allegheny was later rescued by Captain Jean-Luc Picard commanding the USS Enterprise-E. Upon rescuing the Allegheny, Picard discovered a large Borg base. He mounted an assault on the base, destroying it, while taking only minimal casualties. (ST video game: Armada II)