Fluxx: Hand limit zero + trade hands
What will happen is Player A will pass his hand to Player B (should be 2 cards since Player A would have had 0 cards to start the turn, drew 3 and played 1) and since no other player can have cards due to the hand limit Player A gets no cards in return. Once the cards reach Player B's hand the hand limit will kick into action and force him to discard both cards and  return to 0 cards in his hand. At this point the trade action will be fully completed and  Player B will be able to start his turn by drawing 3 cards and playing one of the 3 cards now in hand.

There is also a rule that lets you take a free action of taking the top card of the deck and playing it. This action does not have to happen before you take your last action and is allowed to happen after you have taken your last action and before the next players turn ends. This should make it more clear that the player in this case has to discard the 2 cards.