does -1/-1 counters kill indestructible creature
does -1/-1 counters kill indestructible creature
If a creature's toughness becomes 0 or less due to -1/-1 counters, it will be put into the graveyard (not destroyed) the next time state-based actions are checked. Indestructibility prevents only things that would destroy the permanent that has it, so an indestructible creature will indeed go to the graveyard if its toughness becomes 0 or less.