Varys is removed from the game rather than being sacrificed/discarded to avoid an interaction with discard pile recursion such as Rebuilding. While a copy of Varys is removed from the game, it's perfectly legal to marshal a second copy (provided of course that there isn't a third copy in your dead pile).
Anything that saves from a "discard" effect can save from Varys, so Bodyguard and Duplicates both work.
You cannot initiate Varys' ability and then try to save him (ex: with a duplicate). "If any part of a cost payment is prevented, once all costs that can be paid are paid, the process of initiating the ability or marshaling/playing the card immediately ends without further resolution."