If an affected piece was already blank side up, it gives up its second half-life and retires from the board, to be reborn later. The other player's pieces remain unscathed. Here is a game where one player does not gain from damaging the other. A valuable strategy, in fact, is to use as much as possible the opponent's pieces as partners, to minimize the number of half-lives one has to spend. If a player is entitled to bring in two pieces, there must be two pieces available to bring in.
Some foresight can prevent such an outcome.
It need not even be inflicted deliberately by the other player. The board has sufficient pathways to make purposeful entrapment unlikely. This game is loaded with symbolism and relationships, and it makes for a fascinating lab example of integrated systems. The absence of fear of assault by the opponent also makes possible an especially cerebral, logical strategy. And a typical round of The Power of Two can be played in only about 15 minutes.