No game effect can cause you to win the game or cause any opponent to lose the game while you control Abyssal Persecutor. It doesn’t matter whether an opponent has 0 or less life, an opponent is forced to draw a card while their library is empty, an opponent has ten or more poison counters, an opponent is dealt combat damage by Phage the Untouchable, you control Felidar Sovereign and have 40 or more life, or so on. You keep playing.

If Abyssal Persecutor leaves the battlefield while an opponent has 0 or less life, that opponent will lose the game as a state-based action. No player can respond between the time Abyssal Persecutor leaves the battlefield and the time that player loses the game.

Effects that say the game is a draw, such as the _Legends_(TM) card Divine Intervention, are not affected by Abyssal Persecutor.