It can be argued that Anhura from the musical-in-album-form Razia's Shadow fits this trope. She argues against her father and seems to have the same sense of a greater destiny as Adakias, but she doesn't do anything about it except sit around singing wistfully (Adakias has his share of wistful singing, but he's much more proactive). She's first a damsel when her father refuses to let her marry Adakias, but Adakias rescues her by eloping with her. This causes her to grow ill, and a third of the second act is therefore spent trying to cure her illness. Then once they do, Pallis bursts in, and Adakias sacrifices himself to save her when Pallis attempts to murder her. Depending what you think happened directly after the end of the song and before the narrator's epilogue, Anhura either ends up with Pallis, staying a damsel, just a rescued one, fixes everything herself while Pallis retreats, getting out of the trope, or everything fixes itself without her help, which keeps Anhura thoroughly useless and in this trope.
Subverted in the video of Mean by Taylor Swift. Taylor is shown tied up on railroad tracks by a villain, who is all gloating over her predicament. Not long after, a friend of the villain's comes along, the two villains get drunk, fall asleep, after which Taylor simply gets out of her ropes and heads off.
Sweet Sue in the movie-melodrama parody song "Along Came Jones" (sung by Ray Stevens among others); she keeps getting menaced by Salty Sam and then rescued by the eponymous hero.