Can Yahenni become indestructible after taking lethal damage, and does it die then?

Question

I cast Cruel Entertainment targetting both me and an opponent, who controls Yahenni, Undying Partisan and some other creatures. My own turn ends, and I take control of their turn, in which I attack with Yahenni only. It is blocked by a creature which deals lethal damage to Yahenni.

Now, can the activated ability of Yahenni ("Sacrifice another creature: Yahenni gains indestructible until end of turn.") still be activated after taking lethal damage, so that I can wipe the whole board of the opponent?
If so, does the fact that Yahenni then becomes indestructible negate the fact that it has taken lethal damage in that combat phase (in which the opponent will still have Yahenni on the board)?

Answer 1

There is no way to both use Yahenni to sacrifice all other creatures, and also have Yahenni die due to lethal damage.

Once the creature has actually taken lethal damage, you cannot give it indestructible and save it. It would die the next time state-based actions are checked; and state-based actions are always checked before a player received priority.

However, you can give it indestructible after blockers have been assigned, but before damage is dealt. You would do this in the assign blockers step of the combat phase, which happens before damage assignment. But if you do this, Yahenni will survive. Even if you could use Yahenni's ability after it has received lethal damage, it wouldn't matter, because Indestructible causes lethal damage to have no effect on a creature.

As per monoRed's comment, to get the result you desire, you would need to have a way to kill Yahenni outside of combat. If you (or your opponent) have any direct damage or destruction spells that are instants or abilities, you could activate Yahenni's ability repeatedly to remove all other creatures, and then while those activations are still on the stack, before they have resolved, use the other spell/ability to kill it.

You can see the details of the combat phase steps here: Where can I find a chart or diagram explaining Magic's turn structure?.

Answer 2

You normally either get to sacrifice all other creatures, or can have Yahenni die due to combat damage.

Activated abilities can be activated by a player at any point they have priority. In the scenario you describe, the last opportuinity you have to sacrifice all other creatures that player controls is in the Declare Blockers step, after blockers are declared, as the next step is the Combat Damage step, in which all creatures deal damage and will die due to state-based actions if they have lethal damage marked on them (unless they are Indestructible).

The activated ability itself will be put on the stack as soon as you activate it, meaning whenever you sacrifice a creature, the next thing happening (assuming nothing else is cast or activated in response) is Yahenni gaining Indestructible. Since it's state-based actions that destroy creatures wil lethal damage, and state-based actions don't use the stack, you don't get priority to activate the ability in response.

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Depending on the exact abilities of the other creatures your opponent controls, it's possible to make this work - for example, if your opponent controls a Elesh Norn, Grand Cenobite and Yahenni is a 4/4 because of it, having it dealt 2 damage in the Combat Damage step, then sacrificing all your other creatures, and finally Elesh Norn, will get rid of all creatures, because Yahenni will briefly be a 2/2 again, with 2 damage marked on it, and be destroyed by state-based actions before the ability to grant it Indestructible resolves.