Mirror Universe

• WWizards of the Coast2007-09-16
  Official Ruling
  When the life totals are exchanged, each player gains or loses the amount of life necessary to equal the other player’s previous life total. For example, if player A has 5 life and player B has 3 life before the exchange, player A will lose 2 life and player B will gain 2 life. Replacement effects may modify these gains and losses, and triggered abilities may trigger on them.
• WWizards of the Coast2011-01-01
  Official Ruling
  If an effect says that a player can’t lose life, that player can’t exchange life totals with a player who has a lower life total; in that case, the exchange won’t happen.

Rulings via Scryfall