In 2378, Sphere 634 was one of the few ships the Borg Queen managed to maintain contact with after she'd been infected by Admiral Kathryn Janeway's neurolytic pathogen. The Queen sent Sphere 634 after the USS Voyager, while the ship was hurtling through the Borg transwarp network towards the Alpha Quadrant at amazing velocities. The sphere attacked Voyager, causing the ablative generator's armor integrity to drop to six percent, using the knowledge of the technology from the assimilated Admiral Janeway.
The sphere appeared less than a light year from Earth, where it met the force of 27 Federation starships. It was destroyed by a transphasic torpedo from within, where Voyager laid captured. (VOY: "Endgame")
In the computer game Star Trek: Elite Force II, Sphere 634 captured Voyager and the Hazard Team had to free the ship by destroying the field generators. The Sphere also had a new prototype drone aboard – a member of the Borg from a previously unknown species who appeared not too intelligent, but twice the height and proportionally stronger than a typical Human.