The Palladion belongs to a class of object the Greeks took seriously and modern readers often miss: the image whose physical presence, not the worship offered to it, is what protects a place. It was small, said to have fallen from the sky, and held inside the citadel, and the tradition is that Troy could not be taken while it remained there.
The city falls only after Odysseus and Diomedes steal it. That is a theology of location rather than of devotion, and it travelled. Rome later claimed to hold the same image, kept by the Vestals in the Temple of Vesta, on the argument that Aeneas had carried it out of the burning city, and a Roman could therefore treat the security of the empire as physically stored in a shrine in the Forum. The claim was contested in antiquity, with several cities asserting the genuine article, and no ancient writer could settle it. Troy itself kept a religious standing long after any Bronze Age city there had gone.
Persian and Macedonian commanders sacrificed at the site on their way east, treating it as a place where a campaign could be dedicated, and Rome granted the small settlement at Ilium privileges on the strength of the descent its ruling family claimed from Trojan refugees. The site outlasted its own destruction because the story attached to it was worth more than the walls.