If a player’s starting life total is odd (Commander Vanguard? Sweet.), half that player’s life total will be a fraction, and that’s okay. For example, if an opponent’s starting life total is 41, half that number is 20 ½. If that player’s life total is 20 or less, Anya will have indestructible.
Damage dealt to Anya is tracked even if Anya has indestructible. For example, if Anya is dealt what would be lethal damage and Anya loses indestructible (perhaps because each opponent’s life total is too high), it will be destroyed the next time state-based actions are performed. However, the check for whether a creature dealt damage by a source with deathtouch is destroyed happens only the first time that state-based actions are performed after that damage-dealing event.