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If a creature with a survival ability isn't tapped when your second main phase begins, the ability won't trigger at all. You won't be able to tap it during your second main phase in time to have that ability trigger.

If a creature's survival ability triggers but that creature is untapped when the ability begins to resolve, that ability won't do anything.

If a creature's survival ability triggers but the creature leaves the battlefield before the ability resolves, use its tapped or untapped status as it last existed on the battlefield to determine whether or not the ability will do anything.

If you reveal your entire library and don't reveal a land card, you'll put all revealed cards back in a random order. Since you were never instructed to shuffle your library, abilities that trigger whenever a player shuffles their library won't trigger.

Survival abilities (and other abilities that trigger at the beginning of your second main phase) will trigger at the beginning of the second main phase you take in a turn. They won't trigger during your third, fourth, or other additional main phases in a single turn, if effects somehow cause you to have more than two main phases.