Following a furious battle between Imperial and Alliance forces, the Rebels managed to retrieve the secret information and escape. Unfortunately, the ship and the rest of its crew became prisoners of the Empire.
The corvette was captured by the Motivator, but Rogue Squadron and the frigate Redemptionarrived to recover the data. Although Wedge Antilles and the other Rogues managed to destroy the Motivator,Razor had been drawn into its hangar bay and joined the Star Destroyer in its out-of-control plunge to the surface of Kothlis. Crix Madine and a group of commandos joined the Rogues in reaching the crashed starship and recovered the stolen data before the Motivator's reactor exploded.
Rogue Squadron II: Rogue Leader and X-wing Alliance portray different outcomes as to the Razor's fate. While X-wing Alliance shows the Razor leaving the Battle of Kothlis, Rogue Leader shows the destruction of the Razor and its captor, the Motivator (not Avenger), upon the latter's crash-landing on Kothlis.
There has not been an official retcon to reconcile this, but it's possible that Razor was a group of at least two Corvettes, and each game shows the fate of each one.
The fate of the Razor, which was carrying top secret data, pursued by a Star Destroyer and captured by its tractor beam, then ejecting the plans in an escape pod, is nearly identical to that of Tantive IV and the opening scenes of A New Hope.