A: No, once achieved, their ID is turned over as accomplished. The timeline state can be altered, and it will not affect the fact that that player successfully complete their ID goal.
Archives
Q: What happens if I play Your Parents Never Met on an opponent during ÜberChrononauts, when each player has 2 ID cards?
A: You randomly choose one of the other player’s ID to discard and replace.
Q: Can Voluntary Re-assignment be used to replace ChronoFRED’s mission?
A: Yes. You can also make the Head in a Jar’s Parents Never Meet.
Q: In ÜberChrononauts, what happens to Chrono-FRED or the Head-in-a-Jar when their goal is complete?
A: When you get a FRED/Head victory, you take that Mission/ID for your own, and discard both the Gadget and your own uncompleted Missions/IDs. However, if you have FRED or the Head but accomplish your own Mission or ID, you reveal your card, discard your extra, and then simply retain the Gadget. At that point, it becomes useless to you; but FRED and the Head retain their mission/ID cards, and they stay in your possession. The Head is still who he is, and FRED is still programmed to complete that Mission, so the Gadgets stay in play as usual.
Q: In ÜberChrononauts, can the Chrono-FRED or Head in a Jar allow you to win without completing the other two parts of the game?
A: No. If you accomplish FRED’s Mission and/or the Head’s ID then you simply keep that Mission or ID card as if they were your own. You still need to complete all three win conditions.
Q: In ÜberChrononauts, should a new Mission or ID be drawn upon completion of the first?
A: No. You keep your old one, it’s just face up now. You’re still you, but everyone knows you now, and your mission becomes a reminder of past accomplishments, like a diploma on the wall.
Q: In ÜberChrononauts, can someone Get There First and steal your completed Mission or ID, or Gold Watch?
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.