What happens to a hidden Zhonya's when the unit it's attached to dies during combat?

Ruling: During combat, you retain control of the battlefield until the end of combat even with no units, so the hidden Zhonya's stays until then and can be flipped. Outside of combat, the Zhonya's is trashed immediately if the unit dies.

Sequence:

• If unit is killed with a spell during combat: You retain control through the combat showdown, can flip Zhonya's after the spell resolves, then it goes to base when combat ends
• If unit dies from combat damage: Usually no timing window to flip Zhonya's before combat ends, unless there's a triggered effect like Deathknell that you can respond to
• Outside of combat: Zhonya's is trashed immediately when unit dies

Nuances:

• The combat showdown continues even if all your units are killed by a spell - it doesn't change to a non-combat showdown or move to combat damage step
• Combat damage step is skipped if no units remain, but the showdown still completes normally
• Zhonya's is played directly to base (not to battlefield first)