What is it they are a fan of, though? Just the name? If something is destroyed, and then something else is built and given the same name, is it really the same thing? Likely the location will remain the same though, and that would be an important factor in taking on the old club's identity for the benefit of the new club. Even if it technically will not be the same club, people can comfort themselves by convincing themselves it is the same club, and this is easier if the new club uses the same name, location and wears the same colours.
This does of course raise the question of what do football fans really support when they support a club? The only things which really seem to be constant are the main colours worn, the name, and the location; owners, managers, players, these all change. How much can you change before it ceases to be what the original was? And if the only constant factors are merely superficial, does this not highlight the folly of how emotional some fans get over it all?
Lastly, Vox, what are their motivations as fans? What is it they are loyal to?