Normally, when a playable card is discarded, a player will write Elimination Notes on their hand for the other copy of the card.
However, there is a special case when two copies of the same 1 are discarded. The original Elimination Notes from the discard of the first 1 no longer apply because it is possible that the player has drawn the third copy of the 1 before the second copy could be clued.
Thus, when a player discards the second copy of a playable 1, they should delete all of their Elimination Notes from the first discard and rewrite all of the Elimination Notes on the rest of their hand anew (essentially acting like the second discard was the first discard).
For example, in a 3-player game:
Nothing is played on the stacks.
Alice discards a red 1. Alice writes Elimination Notes on her slot 2, slot 3, slot 4, and slot 5.
On her next turn, Alice discards an unrelated card. She now has Elimination Notes on slot 3, slot 4, and slot 5.
On her next turn, Alice discards another red 1. Normally, she would now have Elimination Notes on slot 4 and slot 5. However, because of the Elimination Rewrite, she instead writes Elimination Notes on slot 2, slot 3, slot 4, and slot 5.
Given enough negative clues on a card (and potentially some ancillary information based on the history of the game), it is possible to narrow down the identity of an unclued card in your hand to possibilities that only include playable cards that are not already touched in someone else's hand.
In this situation, you are expected to blind-play the card.
If a player who is blind-playing into a Layered Finesse skips over a card, they are performing a Layered Jump. This player has deduced that the card they are skipping over is duplicated (or otherwise bad).
The card skipped over in this way will be the next thing discarded, as it is now considered known trash.
If a Layered Jump skips over a card that cannot be in your own hand, then you can determine that it must be a mistake. In this situation, the skipped-over card must be clued directly to re-signify that it is good.