Can Zhonya's be used to react at any time during damage assignment and control which unit survives?

Ruling: No, you cannot use Zhonya's to react during damage assignment or when damage is dealt. You must flip Zhonya's before combat damage (during the showdown while you still have priority). If multiple units die simultaneously to combat damage, the controller chooses which one to save.

Sequence:

• Flip Zhonya's during the showdown before combat damage is assigned (while you have priority)
• Combat damage is assigned in entirety
• Combat damage is dealt simultaneously to all units
• If multiple units die at once, the controller of those units chooses which one to save with Zhonya's

Nuances:

• You cannot react to damage being assigned or dealt because those processes do not pass priority
• The showdown must have ended before damage assignment, so there is nothing to react to at that point
• To play a reaction outside of your turn, you need priority, which requires a chain
• Priority is passed when you explicitly pass it or when a chain item resolves