Frightful Delusion has two distinct effects when it resolves. When it is cast, it must target a spell. When Frightful Delusion resolves, the controller of the targeted spell can pay one mana. If he or she does not, then that spell is countered. Then the controller of that spell will discard a card. This happens even if the mana was paid to prevent the targeted spell from being countered. These two effects are not connected, and the controller of the targeted spell will discard a card regardless of whether or not the one mana was paid.

If Frightful Delusion does not resolve for any reason, then no part of its effect will be applied, and the controller of the targeted spell will not discard a card.