Maybe in a fanfic, Finn's death could be part of a time - traveling accident. He could get caught in a time rift while trying to save someone or something important. His death would then cause a chain reaction in the timeline of Adventure Time. The fanfic could focus on how the other characters try to fix the timeline to bring Finn back or at least come to terms with his loss.
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 Jake might become withdrawn and less likely to go on adventures.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.
One popular story might be one that focuses on how the other characters in 'Glee' deal with Finn's death on an emotional level. They could be struggling to come to terms with the loss and how it affects their performances and relationships within the glee club.
Some write them to explore the darker and more emotional aspects of the Adventure Time universe. Finn is a beloved character, and his death can bring out strong emotions in both the writer and the reader.
Some fanfictions might show the characters crying a lot and being unable to focus on their normal activities like singing in the glee club. They could be constantly thinking about Finn and having flashbacks to their memories with him.
This type of fanfiction is quite heavy. It could depict Rachel's downward spiral leading to her suicide, perhaps due to the overwhelming grief of Finn's death. The writers of such fanfictions might focus on how the other members of the Glee club try to hold on to their own sanity while also dealing with the loss of two important people. It can be a very emotional read, full of heartbreak and a sense of hopelessness at times.
One idea could be exploring how the other characters like Jake deal with Finn's death. Maybe Jake would go into a deep depression at first, as they were such close friends. He might then try to find a way to bring Finn back, leading to all sorts of magical and dangerous adventures.
In the original series, Finn is alive and has all his adventures. But in the fanfiction about his death, the whole tone is much darker. The original is full of light - hearted moments, while the fanfiction is likely to be more solemn and sad.
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.
One common theme is grief. The characters in the fanfiction are likely to be overwhelmed with sorrow. They may also experience guilt, like thinking they could have prevented these tragedies. Another theme could be the shattering of dreams. Finn had his own dreams, and Rachel was so ambitious, and their deaths would mean the end of those dreams for them and also a huge blow to the dreams of the Glee club as a whole.