I'm not sure if there's a specific fanfiction just about Karolina being hurt. However, in general, if you search on popular fanfiction platforms like Archive of Our Own, you might find some stories. Writers might explore her being hurt in various ways, such as during battles or through emotional turmoil within the Runaways group. It could also involve her powers having some sort of negative impact on her, which causes her pain or distress.
One possible plotline could be that Karolina is hurt during a mission when she tries to protect one of the other Runaways. This could lead to a rift in the group as they debate the best way to keep everyone safe in future missions. Another could be that she gets hurt by a new villain who has a weapon that specifically targets her powers. As she recovers, she has to figure out how to adapt and regain her strength.
A really interesting 'Marvel Runaways' fanfiction is 'Among the Runaways'. This one focuses on a particular member of the group and their journey of self - discovery. It has some great action scenes and also some heart - warming moments that make it a great read for fans of the series.
One common theme is the clash of different power sets. For example, when the Runaways cross over with a more established team like the Avengers, their street - level powers and more unorthodox abilities contrast with the big - name heroes' powers. Another theme is the coming - of - age aspect. The Runaways are mostly teenagers, and in crossovers, they often have to grow up fast and learn to work with others in a more complex superhero world.
FanFiction.net is another place to look. There are quite a few 'Marvel Runaways' fanfictions there. However, the quality can vary a bit more compared to AO3. But it's still worth checking out as there are some hidden gems. Just be prepared to do a bit more sifting through the stories to find the really good ones.