Indestructible only protects a permanent from being destroyed — whether by spells and abilities that say 'destroy,' or by lethal damage (CR 702.12b). It does not make a creature immune to all forms of dying.
State-based actions are checked continuously, and one of them (CR 704.5f) states that a creature with toughness 0 or less is put into its owner's graveyard. Crucially, this action does not use the word 'destroy' — the creature is simply moved to the graveyard as a game rule, bypassing indestructible entirely (CR 704.3).
This commonly comes up with effects that reduce toughness, such as -1/-1 counters or spells like Tragic Slip (when its morbid condition is met, giving -13/-13). Even a creature with indestructible will die if its toughness is reduced to 0 or less by such effects.
Example: Your opponent controls a 3/3 creature with indestructible. You cast Dead Weight (−2/−2) on it, making it a 1/1 with indestructible, then cast Festering Goblin's ability targeting it for another −1/−1, making it 0/0. When state-based actions are checked, the creature is put into the graveyard because its toughness is 0 — indestructible does not save it.
In short: indestructible ≠ invincible. Toughness-reduction to 0 or less kills any creature regardless of indestructible.
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.