Does indestructible prevent a creature from dying to a state-based action when its toughness is reduced to zero?

Indestructible only shields a permanent from two specific state-based actions: being destroyed by lethal damage (CR 704.5g) and being destroyed by effects that say 'destroy' (CR 702.12b). It does not protect against every way a creature can die.

When a creature's toughness is reduced to 0 or less — for example by a -X/-X effect — state-based action CR 704.5f applies: the game checks whether any creature has toughness 0 or less, and if so, that creature is put into the graveyard. Crucially, this action says the creature is 'put into the graveyard,' not 'destroyed,' so indestructible offers no protection whatsoever.

CR 702.12b defines indestructible as preventing the permanent from being destroyed, but 'destroyed' is a specific game term. Being placed in the graveyard due to 0 or less toughness bypasses the destruction mechanism entirely, so the indestructible keyword is simply irrelevant to that check.

Concrete example: Your opponent controls an indestructible 4/4 creature. You cast Tragic Slip targeting it, giving it -13/-13 until end of turn (if morbid is active). Its toughness drops to -9. State-based actions check CR 704.5f, see toughness ≤ 0, and put the creature into the graveyard — indestructible does not save it.

The same logic applies to legendary or token rules; indestructible is narrowly scoped to destruction only (CR 702.12b), so players should not assume it is a general 'cannot die' shield.