Since I don't know the exact 'big bear hug story', it could be a child and a teddy bear - like character. Maybe the child is sad and the teddy bear gives a big bear hug to cheer the child up.
Well, the 'big bear hug story' might refer to a tale where a big bear gives a hug. It could be in a fictional context, like in a children's story where the bear hugs a lost little animal to comfort it. Or it could be a real - life inspired story about someone receiving a bear - like, strong and loving hug from someone they care about. Maybe it's a story that uses the 'big bear hug' as a symbol of kindness and protection.
In Junko x OC fanfiction, Junko often retains her complex and unpredictable nature from the original Dangan Ronpa. Her character might be explored in new relationships with the original character (OC). For example, the fanfiction could focus on how Junko's chaotic personality affects the OC, whether it's through manipulation or an unexpected bond forming.
It could be that the cartoon animal is showing self-love or trying to give itself a sense of security. Maybe it's had a rough day and this is its way of coping.