What became of Luke’s X-Wing fighter after he left Bespin at the end of Star Wars: The Empire Strikes Back?

It was moved to a parking facility after an hour or so, to clear the landing pad. It languished in the facility a few weeks, unclaimed. Then a bulletin went out to Cloud City inhabitants informing them that if the vehicle was not spoken for within 30 days, it would be auctioned off. The parking attendants rummaged beneath the seat and found a buck-oh-five in Republic credits.

As Luke was convalescing on the medical frigate, Leia paid him a visit and told him, apologetically, that the deck chief of the Home One has reported Luke as having requisitioned a starfighter that was not returned, because the deck chief is kind of an ass. (The starfighter was originally assigned to Luke during the Rebels’ hasty departure from Hoth, but the deck chief was the one responsible for accounting for them all, fleet-wide.)

Because the Empire had overrun the city of Bespin, even temporarily, it was not possible for the X-wing to be recovered; it had to be assumed the craft was “tagged” and thus could not be returned to the Rebel fleet, or it would give away the fleet’s movements.

So Luke had to fill out some paperwork detailing his encounter with Vader and subsequent rescue and escape, and, being a hero of the Battle of Yavin and held in high esteem by the Rebels’ fighter jocks, was not disciplined.