Whenever a creature's toughness is 0 or less at any point that state-based actions are checked, it is immediately put into its owner's graveyard. This is explicitly covered by CR 704.5f, which states: 'If a creature has toughness 0 or less, it's put into its owner's graveyard.' This applies no matter the source of the reduction — damage, -1/-1 counters, or a continuous effect from a spell or ability.
State-based actions are checked constantly, specifically after every game action and before any player receives priority (CR 704.3). So the moment a continuous effect reduces a creature's toughness to 0 or less, the game checks state-based actions and the creature dies — no player gets a chance to respond first.
Importantly, this is not damage, so the creature does not need to be dealt 'lethal damage' and abilities like Indestructible provide no protection. Indestructible only prevents destruction from damage and effects that say 'destroy' (CR 702.12b). A creature with Indestructible whose toughness drops to 0 via a continuous effect still dies via state-based actions.
Concrete example: Your opponent controls a 2/2 creature with Indestructible. You cast Tragic Slip targeting it for -13/-13. Its toughness drops to -11. State-based actions are checked, and because its toughness is 0 or less (CR 704.5f), it is put into the graveyard — Indestructible does not save it.
This also means regeneration cannot prevent this death, since regeneration only replaces a 'destroy' event (CR 701.15a), and the creature is not being destroyed — it is simply ceasing to exist via state-based action.
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.