If my opponent Piercing Lights my unit at a BF and base and I reveal a Hidden Blade and kill my own unit, does the Piercing Light hit my units in base?

Yes, the Piercing Light will still deal its damage to the unit in the base.

According to RiftJudge FAQ #813 and #1623, the "then" in Piercing Light is a timing instruction, not a condition that requires the first target to remain valid for the second part of the effect to resolve.

Sequence of Events:

1. Opponent plays Piercing Light: They declare their targets (one at a battlefield, one at a base) and put the spell on the chain.
2. You respond: You play your Hidden Blade from Hidden (as a [Reaction]) targeting your own unit at the battlefield.
3. Chain resolves (LIFO - Last In, First Out):
   • Hidden Blade resolves first: It kills your unit at the battlefield.
   • Piercing Light resolves next: Even though its first target is now gone, it proceeds to deal 2 damage to the second target (the unit in your base) because it follows "Do As Much As You Can" (DAMAYC) logic.

Important Note: Piercing Light requires two different units to be targeted when it is played. Because you locked in your targets when the spell was played, the second instance of damage is still directed at the unit in your base, regardless of what happens to the first target.