Often, when Hiccup leaves in fanfiction, it triggers a chain of events that impact the entire Viking community. Maybe they have to find a way to cope without him or work together to bring him back.
Well, it could vary a lot depending on the author's imagination. Maybe Hiccup goes on a solo adventure to find a new land or to face some unknown danger.
In many cases, when Hiccup leaves in fanfiction, it leads to a series of challenges and self-discovery for him. He might encounter new characters, learn valuable lessons, and eventually return to Berk a changed person.