The card discarded by the effect of “Drop Off” is considered to be discarded from your hand, not your Deck. If “Penguin Knight” is the card discarded, its effect will not activate. If “Electric Snake”, “Regenerating Mummy”, or “Fear from the Dark” is the card discarded, its effect will activate.
This card is activated during the opponent’s Draw Phase in response to the opponent drawing a card. It is not chained to the draw.
If a Quick-Play Spell Card is drawn, the opponent may activate it in a chain to “Drop Off” and the effect of “Drop Off” will disappear since the drawn card is no longer in the opponent’s hand.
If the fifth and final piece of Exodia is drawn, the opponent wins before the effect of “Drop Off” is resolved.