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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

Even though your opponents can't lose the game, a player can't pay an amount of life that's greater than their life total. If a player's life total is 0 or less, that player can't pay life at all, with one exception: a player may always pay 0 life.

Other circumstances can still cause an opponent to lose the game, however. An opponent will lose a game if they concede, if that player is penalized with a Game Loss or a Match Loss during a sanctioned tournament due to a DCI rules infraction, or if that player's Magic Online® game clock runs out of time.

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.

Abyssal Persecutor won't preclude an opponent's life total from reaching 0 or less. It will just preclude that player from losing the game as a result.