Does a creature with indestructible still die if it has zero toughness?

Indestructible only shields a permanent from being destroyed — whether by the "destroy" keyword, lethal damage, or effects that say "destroy." It does not protect against all ways a creature can leave the battlefield.

State-based actions, checked continuously by the game, include a rule that puts any creature with toughness 0 or less directly into its owner's graveyard (CR 704.5f). This is not "destruction" — it is a state-based action that moves the creature to the graveyard without using the word "destroy." Because indestructible (CR 702.12) only prevents destruction, it offers no protection here.

Similarly, indestructible does not save a creature from being exiled, sacrificed, or from the "legend rule" — all of which bypass the "destroy" mechanism entirely.

Concrete example: Your opponent controls an indestructible 2/2 creature. You cast Afflict-style effect that gives it −3/−3 until end of turn, dropping it to 2/−1. On the next state-based action check, the game sees its toughness is below 1 and moves it to the graveyard. Indestructible does nothing to stop this.

The key takeaway: indestructible is not the same as "can't die." It only blocks one specific method of removal. Always check how something is causing the creature to leave play — if it's a toughness reduction, indestructible won't help.