Chocobo Crystal Hunt rules question: No cards in hand?

In the first round, the third player's crystal was taken by the second player. The third player then draws a yellow Chocobo. They use yellow Chocobo on the second player and reveals a Bomb monster. The third player must discard that Chocobo, place a card from their hand on the bottom of the deck, and end their turn. The only card in their hand at this point is a Fat Chocobo. Later in the game, if there is no Fat Chocobo in the hand there is almost nothing stopping another player from hunting all the crystals from that player. Can the Fat Chocobo leave their hand, or does it return? Can a player have no cards in hand?