During the reign of the Empire (episodes III-VI) it's conceivable that the lightsabers of dead Jedi survived even if their owners did not. Say a weapon smuggler were to be stopped at a checkpoint by the Empire in possession of a lightsaber, and it was clear that the smuggler was no Jedi. Would possessing the lightsaber automatically be grounds for arrest? Were lightsabers seen as innocent artefacts from a bygone age that could be freely bought and sold on the open market like any other weapon? Were lightsabers seen to be intrinsically linked to the Rebellion - like how being caught in possession of drugs is seen to be implicit evidence of drug usage?
I'm interested in whether this scenario ever happened in canon and, if so, what the result was. But I'm also interested in the broader principle - was the Empire hunting down Force sensitives more generally or was it also looking for non-Jedi with access to old Jedi artefacts?