Does a triggered ability from a permanent that leaves the battlefield still go on the stack?

When a triggered ability triggers at the moment a permanent leaves the battlefield — such as a 'when this dies' or 'when this leaves the battlefield' ability — the ability is placed on the stack even though the permanent is no longer on the battlefield. This is explicitly supported by CR 603.6, which states that triggered abilities can trigger from a zone change and are placed on the stack after the event that caused them.

The key principle is that the game checks the game state immediately before the permanent left to confirm the trigger condition was met. Once it was met, the ability becomes an independent object on the stack and will resolve regardless of what happens to the source (CR 112.7a: an ability on the stack exists independently of its source).

The permanent's last known information — its characteristics just before leaving the battlefield — is used whenever the resolving ability needs to refer back to the card (CR 603.6d). This matters for abilities like 'it had power 3 or greater' or similar self-referential conditions.

Concrete example: Your Solemn Simulacrum (which has 'When Solemn Simulacrum dies, you may draw a card') is destroyed by Murder. Solemn Simulacrum goes to the graveyard, and its triggered ability goes on the stack. Your opponent cannot stop you from drawing the card by destroying the Simulacrum again — it's already gone — because the ability is now independent on the stack.

This also applies to 'leaves the battlefield' triggers on enchantments, tokens, and any other permanent type. Even tokens, which cease to exist on leaving the battlefield, can still have their triggered abilities resolve (CR 603.6, 603.8).