This reminds me of the Greek paradox "Ship of Theseus" which asks the question if every part of a ship is reconstructed over time is it the same ship?

If any subset of the new ship is a subset of the original ship then surely. But this also raises the question if we take a subset and build a new ship. Which is the original?

Another interesting take is to introduce non-physical attributes such as a name of the ship. That way every piece of wood could be changed but the name attribute would still make it a subset