The Green Shadow belonged to the Rodian assassin known as Nashka. It was heavily modified from its stock configuration to be an extension of Nashka's own self and served the assassin well throughout his time as leader of the Dinkos, his days as Vigo in Black Sun, and a good many years after the Battle of Endor.
Nashka desired a ship that could out perform any other, not just in space but also in a planetary atmosphere. He settled on the SoroSuub Planetary Fighter for just that reason. In its stock configuration, the fighter was already dangerous in the right hands, but Nashka saw room for improvement.
By the time Nashka was done, the fighter was perfect for fast and deadly strikes, which was how Nashka preferred to attack. The ship's excellent speed along with its stealth package meant that Nashka could attack without warning and then disappear again before his target could react. Often times Nashka didn't need a second pass.
Nashka would often use the Green Shadow’s numerous modifications to surprise the enemy. His most frequently used trick was retracting the Green Shadow’s wings and using the smaller profile to fool scanners or to fit into gaps no ordinary Planetary Fighter could hope to fly into. More often than not these tricks worked, much to the lamentations of Nashka's enemies.
Somewhat appropriately, the Green Shadow was never destroyed in combat. Instead it received an ignoble end by being blown up on a landing dock on Nar Shaddaa by another assassin’s starfighter.