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The Order of the Stick: Discussed in this strip: Haley is in trouble and Elan wants to rush off to rescue her. However, Durkon stops him, explaining that she is able to take care of herself. And that he is not. If he try to rescue her, he will just get himself killed, and that would make her very sad once she gets back on her own. Elan is forced to leave Haley to her fate. And yes, she does save herself. And Belkar. And Roy's corpse, so it can be resurrected later.
Turned on its head in 8-Bit Theater, by the character of Princess Sara. Sara, through countless kidnapping attempts at the hands of countless villains, has apparently gained enough knowledge and experience to become a competent villain in her own right. She even tries to help Garland, her latest kidnapper, in his battle against the Light Warriors. Sadly, Garland isn't nearly as good at the whole "being a villain" thing as she is. "... but if something's worth doing, then it worth doing right."
Gleefully mocked (if not outright subverted) in Adventurers, where (lead character) Karn's mother (a White Mage) scolds neophyte White Mage, Lumi, for (among other things) "not being taught how to be kidnapped properly."
And in another strip, where Karashi is kidnapped, and has already freed herself and made it back to camp by the time Drecker finds the note left by the kidnapper and announces that they have to rescue her.
Possibly the ultimate aversion in Super Stupor, a supervillain tries to kidnap a superhero's wife, and she brings him to tears, then maims him with a garbage disposal. The hero visits him in hospital, and the villain says he fears for the hero's own safety.
El Goonish Shive "Painted Black" arc. Grace becomes one when she's captured while infiltrating Damien's base. She doesn't stay that way for long, and actually ends up being the one to defeat Damien after he gets her really, really mad.
Ronin Galaxy: This arguably happens twice to Taylor in the first chapter. First when she wants to escape her initial situation, and again after she believes she's out of dodge. Luckily Cecil and Giancarlo manage to track her down and save her (again.)
This happens yet again to Taylor, and Rin in the second chapter. The latter gender-swapping the role.
And another turn: Peach dreams of being the heroine of her own game. Zelda dreams of being the heroine of her own game. Bayonetta, who is the heroine of her game, wants to be the one who gets rescued instead. And have a good dress.
Exiern has Peonie as the recipient of the frequent kidnapping card. Although it wasn't the first or the last time, it seems that Evil Sorcerer Faden was the nastiest as she complained "I was really scared this time". She hasn't managed to stop other people targeting her for an abduction yet though, and Tiff can generally tell what time it is by whether Peonie has been kidnapped yet or not.