I'm not entirely sure which specific 'bts kid story' you're referring to. It could be a story related to BTS when they were kids, perhaps about their early dreams, or some anecdotes from their childhood.
One interesting part could be their first experiences with different music genres as kids. They might have been exposed to traditional Korean music, as well as Western music like hip - hop and pop, and how those exposures influenced their unique musical style today. Another aspect could be their early dance practices. They probably practiced for hours in small studios or even at home, trying to perfect their moves, and those early efforts are part of what makes their performances so amazing now.
There could be a theme of growth and learning. Maybe through the encounter with the hurt kid, the BTS members learn something about themselves or about the importance of helping others. Also, the theme of hope might be present. Their presence and actions could bring hope to the kid who is in a difficult situation.
I'm not sure there are many specific 'drowning kid meets BTS' fanfictions. Fanfiction usually covers a wide range of themes, but this combination seems rather unusual. You could try searching on some large fanfiction platforms like Archive of Our Own and use those key words to see if anything comes up.
One plot could go like this. BTS is on a trip to a beach for a photo shoot. There's a small child who accidentally gets carried away by a strong wave and starts drowning. The members notice and quickly work together. Some hold hands to form a chain to reach the kid while others call for help. After saving the kid, the kid's family is so grateful and the whole incident becomes a big news story, which also spreads the positive image of BTS further.
Well, in this kind of fanfiction, the vampires from BTS might initially be intrigued by the kid reader. They could be protective, seeing the innocence in the kid. Maybe they would shield the kid from other dangerous vampires or supernatural threats in their world.
Finding a specific 'bts meet kid is hurt fanfiction' can be a challenge. Fanfiction is a vast world, and there are so many different stories out there. One thing you could do is to start by looking at the most popular BTS fanfictions and then skim through their summaries to see if any match what you're interested in. Also, consider leaving a request for this type of fanfiction on fanfiction - related forums. That way, other fans who might know of such a story can point you in the right direction.
They would probably be very concerned. Jungkook might be the first to approach her and offer his help. They'd do whatever they could to make her feel better, like giving her a warm hug.
The plot could involve BTS members showing their kind and caring side. They might take the hurt female kid to the hospital, comfort her, and try to find out what happened to her. Maybe they'll also use their influence to ensure her safety in the future.