If a 6 might unit gets targeted with both hits of Falling Star, does the unit live with 3 damage or 0 damage on it?

Ruling: The unit lives with 0 damage on it. It dies after the second hit and is saved by Zhonya's, which clears all damage.

Nuances:

• A 3 might unit would die even with Zhonya's and use it up if it got targeted by both Falling Star hits
• For a 7 might unit hit by Icathian Rain (6 triggers), the first four triggers kill it, Zhonya's saves it and clears the damage, then two more triggers hit it leaving 4 marked damage