The Final Mystery will occur if Doom reaches zero. If this happens, flip the Ancient One sheet, resolve the effect on the back under "The Ancient One Awakens!" immediately, and then treat the text on the back as one final Mystery.
Unlike a normal Mystery, the Final Mystery can run concurrently with another Mystery. However, typically the Final Mystery may not be completed until the other mysteries have been completed.
The Final Mystery is not required to complete most games. Completing the requisite amount of normal mysteries will win the game for the players without the Final Mystery ever occurring. Syzygy is the exception, the players will always encounter the Final Mystery, and the game will end if Doom reaches zero.
Not all Ancient Ones have a Final Mystery. Azathoth will end the game if Doom reaches zero.