Does an indestructible creature die when its toughness is reduced to zero or less?

Indestructible (CR 702.12) means a permanent cannot be destroyed — it survives effects that say 'destroy' and is not put into the graveyard from lethal damage. However, it does not protect against all ways a creature can leave the battlefield.

State-based actions (CR 704.5f) specifically state that a creature with toughness 0 or less is put into the graveyard. This is not the same as being 'destroyed' — it is a state-based action that moves the creature directly to the graveyard, bypassing the indestructible keyword entirely (CR 704.3).

Similarly, indestructible does not protect against being exiled, being sacrificed, or — as relevant here — having toughness reduced to 0 or less. Think of indestructible as a shield only against the word 'destroy' and against lethal damage specifically.

Concrete example: Your opponent controls an indestructible 2/2 creature. You cast a spell that gives it -2/-2 until end of turn, reducing it to a 0/0. When state-based actions are checked, the game sees it has 0 toughness and puts it into the graveyard — indestructible does not save it.

So the answer is yes: any creature, regardless of indestructible, dies when its toughness reaches 0 or less because that is a state-based action, not destruction.