If I play Fallen Star on a unit and it has 1 HP left and then I play Stupefy on it, will the unit end up dying?

Yes, the unit will die.

According to RiftJudge FAQ #2426 and #4751, marked damage and Might are tracked separately. If a unit has marked damage equal to or greater than its current Might, it will die during the next Cleanup phase.

Here is the sequence of events:

1. Falling Star: When Falling Star resolves, it deals 3 damage to the unit. This damage is marked on the unit.
2. Stupefy: You play Stupefy in reaction to Falling Star (or after it resolves). When Stupefy resolves, it reduces the unit's Might by 1.
3. Cleanup: During the next Cleanup phase, the game compares the unit’s marked damage to its current Might. Because the unit had 1 HP remaining (implying its Might was 3, and it had 2 damage marked before Falling Star dealt another 3 damage, or it was a 1 Might unit that took 3 damage), the marked damage will now equal or exceed its reduced Might, causing the unit to die.

This interaction is a standard application of how damage and Might work in Riftbound, as confirmed by multiple RiftJudge FAQs (e.g., #1332, #2426, #4751).