If I have Elder Dragon on field, my opponent casts Star Crossed targeting a unit on the battlefield. Then I use Flurry of Blades. Does the Star Cross resolve, bouncing my Elder to hand, or not because it has no valid target?

Yes, Star-Crossed will resolve and return the targeted units to their owners' hands.

According to Rule 359.3.e.1, a spell resolves even if some or all of its targets are illegal (meaning they no longer meet the targeting requirements or have moved zones). When you play Star-Crossed, it targets a friendly unit and an enemy unit. Even if your Elder Dragon or the other unit leaves the board or changes zones before Star-Crossed resolves, the spell's instructions to return the targets to their owners' hands will still execute for any target that is still legal, and it will be ignored for any that are not.

The Sequence of Events:

1. Opponent plays Star-Crossed: They target a unit on the battlefield. Because it is a [Reaction], it is placed on the chain.
2. You play Flurry of Blades: As a [Reaction], you add it to the top of the chain.
3. Chain Resolution (LIFO - Last-In, First-Out):
   • Flurry of Blades resolves: It deals 1 damage to all units at battlefields.
   • Star-Crossed resolves: The spell attempts to return its targeted units to their owners' hands.
     • If a targeted unit is still on the board, it is returned to its owner's hand.
     • If a targeted unit left the board (e.g., was already destroyed by damage), the instruction to return it is ignored (Rule 359.3.e.5), but the spell still finishes resolving.

Note: The fact that Elder Dragon is the target of Star-Crossed does not make the spell fizzle. As long as at least one of the original targets remains valid—or even if both become invalid—the spell will continue to resolve its instructions as much as possible.