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My opponent played Cry of the Carnarium in MTG Arena. I immediately played Unbreakable Formation after. The intended result was for my creatures to not die or get exiled, but they did. Shouldn't Unbreakable Formation resolve, granting me indestructible until end of turn?

The card Unbreakable Formation will not generally save your creatures from dying from Cry of the Carnarium, because the ability Indestructible does not save creatures from dying from toughness loss.

The ability Indestructible is defined in rule 702.12b:

A permanent with indestructible can't be destroyed. Such permanents aren't destroyed by lethal damage, and they ignore the state-based action that checks for lethal damage (see rule 704.5g).

The rule it references, 704.5g, is part of the State-based action rules:

If a creature has toughness greater than 0, and the total damage marked on it is greater than or equal to its toughness, that creature has been dealt lethal damage and is destroyed. Regeneration can replace this event.

The previous rule, 704.5f, says this:

If a creature has toughness 0 or less, it's put into its owner's graveyard. Regeneration can't replace this event.

As you can see, if a creature takes damage greater than or equal to its toughness, it is "destroyed", so Indestructible can stop it. But if a creature loses all of its toughness, it is just put into the graveyard, so Indestructible doesn't do anything about that.

Magic Arena displays damage the same way it displays toughness loss, but they are not the same thing.

Indestructible does not save a creature from dying due to having 0 toughness. It only prevents creatures from being destroyed.

702.12. Indestructible

702.12a Indestructible is a static ability.

702.12b A permanent with indestructible can't be destroyed. Such permanents aren't destroyed by lethal damage, and they ignore the state-based action that checks for lethal damage (see rule 704.5g).

Dying as a result of having 0 toughness is not being destroyed. A creature with 0 toughness dies because of this state-based action:

704.5f If a creature has toughness 0 or less, it's put into its owner's graveyard. Regeneration can't replace this event.

Also see this definition of destroyed in the rules:

701.7. Destroy

701.7a To destroy a permanent, move it from the battlefield to its owner's graveyard.

701.7b The only ways a permanent can be destroyed are as a result of an effect that uses the word "destroy" or as a result of the state-based actions that check for lethal damage (see rule 704.5g) or damage from a source with deathtouch (see rule 704.5h). If a permanent is put into its owner's graveyard for any other reason, it hasn't been "destroyed."

Similarly, you cannot use regeneration to prevent a creature from dying this way.

Unbreakable Formation did make your creatures indestructible. Unfortunately, that wasn't enough to save them.

"Indestructible" means that lethal damage and 'destroy' effects won't destroy your creatures. However, if a creature had zero toughness it dies as a state-based-effect, and that isn't prevented by indestructible. Cry of the Carnarium reduces the power and toughness of your creatures, dodging indestructible.

Arena confuses this by showing damage as if it was reducing the toughness of the creature, but in actuality the effects are distinct. A 2/2 with two damage still has 2 toughness, but a 2/2 with -2/-2 has 0 toughness.

(Technically speaking, death by lethal damage is also a state-based-effect, but it's one that is specifically protected against by indestructible. )