Does a triggered ability still trigger if the permanent that has it leaves the battlefield before the trigger condition is met?

Triggered abilities only function when the permanent is in the zone where that ability is active. For most permanents, triggered abilities work on the battlefield. If the permanent has already left the battlefield before the triggering event occurs, the ability simply does not trigger — there is no longer anything to 'watch' for the condition. This is established by CR 603.1 and CR 112.6a.

CR 603.1 states that triggered abilities trigger whenever their trigger event occurs and the ability is 'on' — meaning the source must be in the correct zone at the moment the trigger event happens. CR 112.6a confirms that abilities of permanents only function while the permanent is on the battlefield, unless the ability or rules specifically say otherwise.

There are narrow exceptions: some abilities explicitly work from the graveyard or other zones (e.g., 'When this card is put into a graveyard from anywhere…' or abilities with 'dies' triggers). Those are worded specifically to function from a different zone or at the moment of leaving, per CR 603.6.

Concrete example: Your opponent controls a creature with 'Whenever you draw a card, this creature gets +1/+1 until end of turn.' You cast a spell that destroys that creature, and in the same spell's resolution you draw a card. If the creature is already in the graveyard when you draw, the triggered ability does not trigger — the creature was gone before the draw event occurred.

The key takeaway: the permanent must exist in the correct zone at the exact moment the trigger condition is met. If it left before that moment, the trigger simply does not happen.