Lands ravaged, cities in ruins, so many lives sacrificed, and yet there was no other word for it but victory.

Near-Death Experience

At the beginning of your upkeep, if you have exactly 1 life, you win the game.

From the Vault: Lore

Rise of the Eldrazi

In a Two-Headed Giant game, anything that cares about your life total checks your team’s life total. You’ll win the game if your team has exactly 1 life.

This ability has an “intervening ‘if’ clause.” That means (1) the ability triggers only if you have exactly 1 life as your upkeep begins, and (2) the ability does nothing if your life total is anything other than 1 by the time it resolves.