Does a triggered ability still resolve if the permanent that created it leaves the battlefield before the trigger resolves?

Once a triggered ability has triggered and been placed on the stack, it becomes an independent object separate from its source. Per CR 112.7a, the ability continues to exist on the stack even if the permanent that generated it leaves the battlefield before the ability resolves.

This is sometimes called the 'leaves-before-resolving' principle. The key rule is CR 603.8: if a triggered ability's source is no longer in the zone it was in when it triggered, the ability can still resolve normally. The game simply checks whether the ability's effects are still applicable at resolution time.

There is an important nuance: if the ability's resolution requires targeting and the target is illegal when it resolves, it will be countered by the rules (CR 608.2b). But the source leaving the battlefield alone is not enough to stop the trigger.

Concrete example: You attack with Tarmogoyf-sized creatures, and your opponent controls a Solemn Simulacrum. They block and Solemn Simulacrum dies, triggering its 'draw a card' ability. Your opponent then destroys the artifact on their side (it's already dead). The triggered draw ability is already on the stack — it resolves and your opponent draws a card, regardless of Solemn Simulacrum being in the graveyard instead of the battlefield.

In short: triggered abilities 'leave the nest' the moment they go on the stack. Their source's zone change afterward is irrelevant to whether they resolve (CR 112.7a, 603.8).