Harmy said:
I think the Falcon would have been donated to some war museum
I can already see the climactic battle inside the museum, where the bad guy escapes...
"Oh no, he's getting away!" - "Wait, isn't that the old ship I used to fly?" - "It sure is, gramps... let's go!"
... and the good guys crash the Falcon out of its display box (or display hangar) to go after him.