If an opponent gains control of your creature and it dies, does its leaves-the-battlefield trigger use the last known information from before it died?

When a permanent leaves the battlefield, any triggered abilities that trigger on that event use last known information (LKI) — meaning the game looks at the object's characteristics and status as they existed on the battlefield immediately before it left. This is established in CR 603.10.

So if your opponent has gained control of your creature and that creature then dies, the leaves-the-battlefield trigger uses LKI from just before death. At that moment, your opponent controlled the creature, so the trigger is controlled by your opponent (since triggered abilities are controlled by whoever controlled the permanent when it left, per CR 603.6a).

The creature's characteristics — its power, toughness, name, abilities, color, etc. — are also read from that last known state. If it had +1/+1 counters or enchantments on it just before it died, those facts are part of its LKI.

Concrete example: You control Solemn Simulacrum, but your opponent steals it with Threaten and attacks. It dies in combat. The "when Solemn Simulacrum dies, you may draw a card" trigger goes on the stack under your opponent's control (they controlled it when it died), so your opponent draws the card — not you.

Note: LKI only applies to answer questions about the object that left; it cannot be used to apply continuous effects after the permanent is gone. The core rule is CR 603.10, with trigger control governed by CR 603.6a.