Regarding Snape's Occlumency in fanfiction, one aspect that's often explored is how it relates to his past traumas. Maybe his difficult childhood and the bullying he endured made him develop Occlumency as a way to retreat into his own mind. In fanfic, his Occlumency can be a key to unlocking his deeper emotions. For instance, a skilled Occlumens like Snape may have buried his love for Lily so deep that only in the most extreme situations does it start to surface, and this can be a really interesting plot point in fanfiction.
Fanfiction often takes Snape's Occlumency and runs with it. It might show his Occlumency as a form of self - preservation. In the wizarding world full of mind - readers and legilimens, his ability to close off his mind is crucial. In some fics, Snape may have developed his Occlumency not just to protect himself from Voldemort but also from the judgment of his peers at Hogwarts. His Occlumency could be seen as a shield that he has built over the years, and fanfic writers love to explore what lies behind that shield.