A: No. The flipped up card (Mission or ID) or the symbolic Gold Watch is only an outward, physical representation of the work that you’ve done. It’s the work that matters. No one can steal the work you’ve accomplished (nor can they trade it out with New Mission). The work itself is done, past, finished… intangible, therefore unstealable (and unsellable*). The cards mentioned are only an indications of the work, not the work itself.
* The collectors who buy up Artifacts are not interested in it for any Missions (the Midas Mission, Futuristic Alchemist) OR the Sell An Artifact “Midas Bonus”. As another FAQ posits: it’s probably electroplate anyhow.