If a monster with an effect that includes destroying a card(s) is affected by Fiendish Chain or if a Skill Drain applies its effect on the field and attempts to activate its effect, Stardust Dragon can be activated as a chain and it will destroy that monster. That's because Stardust's only prerequisite is the activation of an effect that includes destroying a card(s) on the field, something that both Fiendish Chain and Skill Drain cannot prevent. As long as that monster can activate its effect (regardless of what would happen in its resolution) Stardust Dragon can activate and negate-destroy it.