Does Ward trigger if a spell or ability targets a permanent and then becomes illegal before the Ward trigger resolves?

Ward (CR 702.167) triggers the moment a spell or ability targets the permanent with Ward — specifically, Ward triggers when that permanent becomes the target (CR 702.167a). The trigger goes on the stack immediately after the spell or ability that caused it. At this point, Ward has already triggered successfully.

The more relevant timing question is what happens if the original spell or ability loses its target before Ward's trigger resolves. Under CR 608.2b, when a spell or ability tries to resolve, the game checks if all its targets are still legal. If the original spell has no legal targets remaining, it is countered by game rules before it ever resolves — meaning Ward's trigger, while it may still resolve and demand payment, becomes somewhat moot because the original spell is already gone.

Conversely, if Ward's trigger resolves and the opponent does not pay the Ward cost, the original spell or ability is countered (CR 702.167a). If they do pay, the original spell proceeds normally (assuming targets are still legal at resolution).

Concrete example: Your opponent casts Lightning Bolt targeting your creature with Ward {2}. Ward triggers. In response, you use another effect to give your creature hexproof. When Ward's trigger resolves, your opponent must pay {2} or the Bolt is countered. Even if they pay, the Bolt is then countered on resolution anyway because hexproof made the target illegal (CR 608.2b). Ward still triggered and resolved normally — the hexproof issue is handled separately at resolution.

So Ward always triggers upon targeting; whether the original spell survives to resolution is governed by the legality-of-targets rules (CR 608.2b), not by Ward itself.