If I use Falling Star on a unit and they play Thrill of the Hunt, does the Falling Star still go through?

Yes, the Falling Star still resolves, but the outcome for the target depends on whether it remains on the board.

According to the rules regarding targeting (Rule 359.3.e.7 and the clarification on Alpha Strike/targeting logic), once a spell targets a unit, a targeting relationship is created. As long as that unit remains on the board, the spell will resolve against it even if the unit changes locations.

However, Thrill of the Hunt moves the unit to a non-board zone (Banishment) before returning it to a battlefield. Because the unit is moved to a non-board zone, it ceases to be the same game object. Therefore, the targeting relationship is severed.

Here is the breakdown:

1. Chain Start: You play Falling Star, targeting the unit.
2. Reaction: The opponent plays Thrill of the Hunt as a [Reaction].
3. Chain Finalization: The stack (chain) is now: Thrill of the Hunt (top), Falling Star (bottom).
4. Resolution (LIFO):
   • Thrill of the Hunt resolves: The unit is banished and then played again. Because it moved to a non-board zone, the "arrow" of the Falling Star target is removed (as per Rule 359.3.e.7 and the Alpha Strike clarification).
   • Falling Star attempts to resolve: Because the specific unit it was targeting was moved to a non-board zone and is no longer the same game object, the targeting restriction is severed. The instruction to "Deal 3 to a unit" for that specific targeting instance fails (mistargets).

If you chose the same unit for both instances of damage from Falling Star, and that unit was the one affected by Thrill of the Hunt, neither instance of damage will hit the unit. If you chose a different unit for the second instance, that second instance will resolve normally against its chosen target.