New Redemption Grab Bag now includes an assortment of 500 cards from five (5) different expansion sets. Available at Cactus website.
I think the rule is that guards follow sites. If that's true, then I imagine curses do as well, although there really isn't a precedent to this.
i see no reason it would not follow the site.
However, if the Curse is deactivated or discarded, then it would return to the owner's artifact or discard pile.