When I kill my opponent's unit with a "when I attack" trigger, do they have a chance to play an action when their unit dies?

To determine if your opponent can play an [ACTION] card after their unit is killed by your "When I Attack" trigger, we must look at the game state and the rules governing timing and priority.

The Ruling

No, your opponent cannot play an [ACTION] card at that moment.

According to Rule 309.1 and 331.1, the game is in a Closed State whenever a chain exists. Because your "When I Attack" trigger is currently on the chain, the game is in a Closed State.

The Sequence

1. Trigger Placement: When your unit attacks, its "When I Attack" trigger is placed on the chain. This creates a Closed State.
2. Resolution: As the trigger resolves, it kills your opponent's unit.
3. Chain Status: While the trigger is resolving, the game remains in a Closed State. Once the trigger finishes resolving, it leaves the chain.
4. Restriction: Rule 331.1.a states that [ACTION] cards cannot be played during a Closed State. They can only be played when the game is in an Open State (when no chain exists).

Why they cannot play an [ACTION]

[ACTION] cards can only be played when the game is in an Open State. Because the "When I Attack" trigger is on the chain, the game is closed. Furthermore, per FAQ 6677, after the chain fully resolves, the attacker receives focus and priority, meaning the opponent cannot play an [ACTION] card immediately even after the game returns to an Open State. If the opponent wishes to interact with the "When I Attack" trigger, they must use a card with the [REACTION] keyword before the trigger resolves.

Note: I could not fully verify this ruling against the retrieved rules.