Falleen's Fist served as the personal skyhook for Black Sun's supreme leader, Prince Xizor. In contrast to the Emperor, who stored his most valuable items on his skyhook, Xizor chose to house his most precious treasures within his ground-based palace. This skyhook boasted Xizor's own private fleet, which included corvettes, frigates, and a multitude of refurbished fighters. The command deck was constructed with transparisteel plating all around, providing a 360-degree unobstructed view of the surrounding space for the commander.
During 3.5 ABY, Dash Rendar, Lando Calrissian, Chewbacca, and Luke Skywalker infiltrated Xizor's Black Sun palace to liberate Leia, who was being held as a prisoner. While en route to the landing platform to finalize the rescue operation and make their escape, Lando, acting on impulse, deposited a thermal detonator into a waste disposal chute, effectively sealing the palace's fate. This ensuing turmoil aided the rebels in their getaway, while Xizor utilized his exclusive express turbolift to ascend to the top and flee aboard the Virago to his skyhook. En route, he issued orders to his fleet to either obliterate or capture the Millennium Falcon, which carried the infiltrators, thus executing his scheme to eliminate Skywalker.
During the Battle over Coruscant, Darth Vader gave the order for the Executor to destroy the skyhook, as Xizor was attempting to assassinate Luke Skywalker, who was aboard the Millennium Falcon along with his StarVipers. The skyhook was obliterated, resulting in Xizor's death.
In the video game Shadows of the Empire, a different depiction of the battle is presented, granting Dash Rendar a more prominent role. While a Star Destroyer is present and bombarding the station, Dash actually pilots his Outrider into the Skyhook, echoing the Battle of Endor, and eliminates the core from within.
The skyhook is featured in certain cards from the 1996 Topps Star Wars: Shadows of the Empire collection, exhibiting a similar appearance to the one in the video game, characterized by four elongated, hollow shafts extending from a central cylindrical core in all directions, into which Dash Rendar actually flies. This visual representation is also adopted in the Star Wars Galaxies Trading Card Game. The comic book Shadows of the Empire 6 diverges from this depiction, portraying the skyhook as a crimson space station with a primary body shaped like a saucer.