While Indestructible cards can't be killed by damage and ignore damage checks, their toughness outside of damage still needs to remain about zero for them to stay alive. This makes niche removal spells like Tragic Slip”especially powerful against Indestructible cards.

What kills an indestructible creature?

A creature with indestructible can die as a result of anything that is not damage (Lightning Bolt) and does not explicitly use the word 'destroy' (Doom Blade). And of course, they can be exiled, returned to their owner's hand, or put back into their owner's library.

Does sacrifice destroy indestructible?

Indestructible only means it can't be destroyed, by either effects that say "destroy" or by lethal damage. Sacrificed permanents still go to the graveyard, as do 0 toughness creatures, regardless of whether or not they are indestructible.