If you play a hidden card and same turn your unit at the battlefield dies, can you react to save the hidden card?

No, you cannot react to save a hidden card if you hide it and your last unit at that battlefield dies on the same turn.

According to Rule 811.1.b, a card hidden using the Hidden keyword gains [Reaction] only "Beginning on the next turn." Because the card does not have the [Reaction] keyword on the same turn it is hidden, it cannot be played as a reaction to your unit dying during that same turn.

Furthermore, as established in RiftJudge FAQ #1854, hidden cards can never be played the same turn they are hidden. If you hide a card and subsequently lose your last unit at that battlefield on the same turn (causing you to lose control of the battlefield), the hidden card is trashed without an opportunity to be played.

To summarize the mechanics:

1. Timing Restriction: Hidden cards only gain the [Reaction] property on the turn after they are hidden (Rule 811.1.b).
2. Same-Turn Limitation: Because the card lacks [Reaction] on the turn it is hidden, it cannot be used to respond to game events (such as a unit dying) that occur before your next turn.
3. Loss of Control: Once your last unit at a battlefield dies, you immediately lose control of that battlefield (outside of a contested showdown), and any card hidden there is moved to the trash (RiftJudge FAQ #4628).