Finn might initially go into denial. He could keep expecting Jake to just pop back up like he always does. Then he'd probably get angry, at himself or at whatever caused Jake's death. Eventually, he'd start to accept it and try to honor Jake's memory by being a better hero.
In the fanfic, Finn could cope by throwing himself into adventures. He'd think that by doing the things they used to do together, he could keep Jake's spirit alive. He might also talk to Jake's family a lot, sharing stories and memories. This would help him deal with the pain. And he could start writing in a journal, documenting his feelings and his journey without Jake. This would be a way for him to process his grief.
Well, perhaps in the fanfic, Jake's death could lead to a change in the balance of power in Ooo. Evil forces that were previously held at bay by Jake's strength start to emerge. Maybe the Ice King, instead of seeing Jake as an obstacle to his schemes regarding Princess Bubblegum, now has free rein. Finn would have to step up in a big way, but without his best friend, it would be extremely difficult. He may struggle with feelings of guilt, thinking he could have saved Jake.
Jake would be devastated. He and Finn are best friends. Jake might become withdrawn and less likely to go on adventures. He could also become overprotective of Finn's memory. Princess Bubblegum would likely be deeply affected too. She might feel guilty if she couldn't use her scientific knowledge to save Finn. She could also be motivated to find a way to bring him back. Marceline would probably be very sad and angry. Her relationship with Finn was special, and his death could make her more cynical about the world.
Well, it could be about the kids going on their own crazy adventures. Maybe they inherit Finn's bravery and Jake's shape - shifting abilities and use them to save the Land of Ooo from a new threat.
One interesting fanfiction could be about Finn and Jake going on a quest to a mysterious new land that wasn't explored in the show. Maybe they encounter a new type of magical creature that challenges their friendship and they have to work together to overcome it.
It could be an old enemy of Finn and Jake who has come back to take revenge on their kids. Maybe the Ice King's descendants or something related to him.
You can start by checking out popular fanfiction websites like Archive of Our Own. Just type in 'Adventure Time Finn x Jake' in the search bar and you'll get a list of relevant stories. Look for ones with high ratings and a lot of positive reviews.
First, think about the characters. Know Finn's adventurous spirit and Jake's laid - back but loyal nature. Then, come up with an interesting plot. It could be something as simple as them finding a lost treasure in the Land of Ooo. Next, write in a style that matches the show, with a bit of humor and lots of action.
One interesting fanfiction could be about Finn and Jake going on a new, never - before - seen adventure in a strange magical land. Maybe they encounter a new type of magical creature that challenges their friendship and they have to work together to overcome it.
One great theme is their friendship adventures. Stories that focus on their new quests and how they support each other through different challenges are always interesting. Another theme could be how they grow together as characters over time.
One way is to show them sharing their secrets. Lady Rainicorn could tell Jake about her family in the Rainicorn Kingdom and Jake could share his dreams for the future. They could also have arguments over small things like what to have for dinner, which shows their closeness and comfort in being honest with each other. Then, they make up and their bond becomes stronger. Also, they can protect each other from danger. When Jake is in trouble, Lady Rainicorn uses her horn's powers to save him and vice versa.