The two seem to be on good terms with each other after the events of Chapter 2, when Fuyuhiko is intent on changing himself. They are also willing to stay and focus on their friends that catch Despair Disease in Chapter 3. Though initially, Fuyuhiko did not attempt to form a friendship with Hajime, their relationship changes relatively in the end.
Fuyuhiko considered Hajime as the "Ultimate Counselor" due to his nature that give the students confidence to endure everything that they have. In his last Free Time Events, the two of them did a sakazuki, a Japanese ritual of exchanging cups to symbolize sworn brothers and pledge loyalty.
The ship sailed as a result of the friendly interactions between Hajime and Fuyuhiko, which the two got to have more later on thanks to both surviving the Killing School Trip. Fuyuhiko's friendship ritual with Hajime from their Free Time Events has also helped to further fuel the ship. Fanarts or fanfictions would often reference their interactions from said Free Time Events, especially the exchange of cups symbolizing brotherhood.
However, in spite of this, the ship is not that popular. The main reason behind this is the huge amount of Ship Tease between Hajime and Chiaki and Fuyuhiko and Peko, making those two the primary shipping choices for the characters involved in this ship. Hajime is also heavily shipped with his rival, Nagito Komaeda. Finally, as a result of their friendship being more fleshed out, Soul Friends is the more common ship for Hajime and his fellow surviving male friend.
Initially, with Fuyuhiko being distanced from the group, being a blonde guy wearing a suit like Byakuya, and being from an influencial family, many fans were misled to believe that Fuyuhiko would be the Rival character to Hajime, thus creating a FoeYay ship for the two. However, with the reveal of Nagito's true colors and Fuyuhiko's character development, such dynamics changed to Komahina instead.
- Fuyuhiko's relationship with Hajime on Danganronpa Wiki
- Hajime's relationship with Fuyuhiko on Danganronpa Wiki