Think of a scenario similar to your classic fairytale, where a damsel in distress is rescued by the prince, and she falls in love with him. Is there a name for this as a syndrome or similar? Nightingale syndrome seems to come close, but that seems to be specifically for when someone falls in love with their caregiver. I'm not sure if it applies to a rescuee falling in love with their rescuer.
Some clarification: The term I'm after wouldn't necessarily imply the rescuer and rescuee form a relationship. Merely that as a result of being rescued the rescuee forms an attachment to their rescuer. It might be unrequited. And it wouldn't necessarily involve any sort of inappropriate behaviour, such as the rescuee stalking the rescuer, or the rescuer taking advantage of this effect to form an inappropriate relationship. If anything, the rescuer may recognise the rescuee's feelings are just due to this effect, rather than being genuine, and therefore use this as a reason to rebuff any advances from the rescuee, until such time as the effect has faded. Similar concepts include a patient developing a crush on their nurse (Nightingale Syndrome/Effect), or a student developing a crush on their teacher (transference effect?).
Also, it doesn't need to include the word 'syndrome' or similar. It would also be acceptable if it is a more general term that applies to a number of situations, not just the rescuer-rescuee scenario I've described above.
If such a term doesn't exist, it could perhaps be called something like 'damsel in distress effect', although ideally without implying the rescuee is helpless or female.