I think he puts his card on bottom of his library and draws a new one. However he is not able to take another.
Player 1 has Leovold and Teferi's Puzzle Box on the Battlefield.
Player 2 starts with his draw phase and has no card in his hand.
Therefore "nothing" happens with the Puzzle Box and he only draws a card. Am I right or did I miss something? Do you feel this combo is that strong?