When I trigger Baited Hook, does my opponent have a window to use Star Crossed on the unit I chose to cancel Baited Hook?

Yes, your opponent has a window to use Star-Crossed in response to your activation of Baited Hook.

The Sequence

1. Activation: You activate Baited Hook during your Main Phase by paying its cost and declaring a friendly unit as your target. Baited Hook is placed on the chain.
2. State Change: The game state changes from Open to Closed because there is now an item on the chain.
3. Reaction: Your opponent can play Star-Crossed as a reaction to your activation. Because it is a [Reaction] spell, it is legal to play in this Closed state. Star-Crossed is placed on top of the chain.
4. Resolution (LIFO - Last-In, First-Out):
   • Star-Crossed resolves first, returning your targeted friendly unit and an enemy unit to their owners' hands.
   • Baited Hook attempts to resolve next. However, because the unit you targeted is no longer on the board, it cannot be "killed."

The Result

According to RiftJudge FAQ #10587 and Rule 359.3.e.12, since the unit was not killed (sent to the trash via the ability's instruction), the reference to "the killed unit" returns a null value. You will still perform the instruction to look at the top 5 cards of your main deck, but you will be unable to play a unit because you cannot satisfy the "Might up to 1 more than the killed unit" requirement. All 5 cards will be recycled.

This interpretation is based on the interaction between targeting rules and the specific mechanics of Baited Hook as clarified in multiple RiftJudge FAQs (e.g., #10587, #10345, #4379).