This question takes me back to my peak Naruto fandom days. The Sasuke/Karin dynamic always seemed to exist in this weird space between 'what could have been' and 'what the actual hell canon.' From what I've seen, the most common storyline by far is the post-Fourth Shinobi World War 'what-if' where Sasuke, on his redemption journey, returns to Konoha and actually acknowledges Karin's feelings—and his own. It usually starts with him finding her again, often after she's established herself independently as a sensor-nin somewhere else, which I always appreciate. There's a strong tendency to explore the Uzumaki connection, making their bond about shared heritage and loneliness rather than just her obsessive crush.
A massive chunk of fics are 'Sasuke goes back in time' variants. He wakes up in his 12-year-old body after the war, determined to fix everything, and a key part of his plan involves saving the Uzumaki clan early or specifically protecting Karin from her terrible childhood in the Grass. It's a power fantasy, sure, but it's satisfying to see her get the rescue canon denied her. Less popular but more interesting to me are the darker AUs where Karin never leaves Orochimaru, and they become a twisted power couple running the Sound Village together. Those fics often have a gothic, psychological horror edge that really works with their characters.