If a battlefield has a vex, and you play a master Yi unstoppable at level 16 (it enters ready), can the vex still stun it?

Yes, Vex, Apathetic can still stun Master Yi, Unstoppable even at Level 16.

Reasoning

• Programmatic Selection vs. Choosing: Master Yi, Unstoppable's Level 16 ability states: "I can't be chosen by enemy spells and abilities." However, Vex, Apathetic's ability does not require you to "choose" or "target" a unit. It uses programmatic selection—the ability automatically identifies the unit that triggered the condition ("When an opponent plays a unit").
• Protection Bypass: According to RiftJudge FAQ #8772 and #8685, protection from being "chosen" only applies to effects that require a player to manually select a target. Because Vex's ability automatically identifies the unit based on the trigger event, it bypasses this protection.

Sequence of Events

1. You play Master Yi, Unstoppable.
2. Vex, Apathetic's triggered ability activates because an opponent (you) played a unit while Vex is at a battlefield.
3. The ability programmatically selects the unit that was just played (Master Yi).
4. Because the unit is programmatically selected rather than chosen, it is not considered a target, and Master Yi's protection does not apply.
5. Master Yi is stunned and cannot move for the remainder of the turn.

This is my interpretation based on the established mechanics of programmatic selection versus targeting. No official FAQ exists for this specific interaction with Master Yi, but it follows the established rulings for Vex, Apathetic interacting with other units that have "cannot be chosen" protection (such as Ruin Runner or Baron Nashor).