MTG: Indestructible creature with both damage and -1/-1 counters
It does not.

An indestructible creature will die from having 0 toughness.  It will not die from lethal damage (damage greater than or equal to its current toughness).

In your example, you have indestructible 2/2 (because of a -1/-1 counter), and it has 2 damage marked. It has taken lethal damage (as it has 2 toughness and 2 damage), but has toughness greater than 0, so it does not die.