Spike's claims in Buffy fanfiction have a profound impact on the story. When he claims something, it can shift the power dynamics. Say he claims to be more powerful than a new villain in the fanfic world. This could lead to him taking on more dangerous tasks, which in turn affects Buffy's actions as she may have to either support him or try to stop him from getting killed. His claims about his relationship with Buffy can also change the emotional tone of the story. If he claims they are soulmates, it can bring a sense of fatedness to their interactions and influence how the story unfolds in terms of their relationship development and the reactions of other characters.
Spike's claims can add drama. If he claims to be Buffy's true love, it can create love triangles or other relationship tensions.