does falling star hit

Short answer: yes, in almost every case — Falling Star keeps hitting unless the target left the board entirely or the spell itself was countered.

Falling Star reads "Deal 3 to a unit. Deal 3 to a unit," and it doesn't care where the unit is. If the target is recalled/moved to Base in reaction, it's still the same game object, so both instances still land (FAQ #1958). If the unit changes to a non-board zone instead — returned to hand, killed to trash, banished — it's a different object and takes 0 (Rule 359.3.e.2/.4); you still do as much as you can with the other instance (FAQ #12764). The other stop is a counter like Not So Fast, which removes the whole spell and both damage instances.

One edge case: if the unit becomes untargetable by Falling Star before resolution, it mistargets and is unaffected (Rule 758.1).

What's the specific board state? If you tell me which unit and what moved where, I can pin it down.