Stories about a man rescuing a woman from danger or death have been around for a long time. And, as you know, they are still with us today. We won't even list examples, because you've probably already thought of more than we could ever name. (Think any superhero movie ever made.)
In Greek mythology, "guy saves girl" stories abound. Perseus rescues Andromeda from a sea monster. Hermes is sent (on behalf of Zeus) to save Persephone from Hades. And of course, Orpheus, in lovesick hero mode, attempts to save Eurydice from her premature death.
Traditionally, the maidens in these myths are young, beautiful, innocent, and for some reason, totally incapable of saving themselves. They are not allowed to make their own decisions, and usually don't speak very much. In the versions of the Orpheus and Eurydice myth penned by Virgil and Ovid, Eurydice says very little, isn't given a much of a backstory, and is never asked if she actually wants to be rescued by Orpheus (although, to be fair, anyone stuck in the gloomy Underworld would probably want to escape it).
In modern versions, Eurydice is typically a more three-dimensional character, with thoughts and feelings of her own: check out Sarah Ruhl's play Eurydice for an example.