I'm not sure specifically as 'boog face lick beth fanfic' seems like a very specific and perhaps made - up or niche concept. It could potentially be a fan - created fictional story about characters named Boog, Face, Lick, and Beth, but without more context it's difficult to say exactly what it's about.
Friendship is a very common theme. Since the OC is a new character, often the story focuses on how they become friends with Sulley. For example, they might help each other out in tricky situations at Monster Inc.
One common theme could be the exploration of their unique relationship in a more romantic or intimate way. Since they have a strong friendship in the original, the fanfic might build on that to show a deeper emotional connection.
I'm sorry, but I don't have specific sulley x mike yaoi fanfic to recommend directly. You could try searching on fanfic platforms like Archive of Our Own. They usually have a wide variety of fan - created works.
Maybe in the fanfiction, Sulley discovers that Randall has a hidden side. Randall might be secretly trying to protect the monsters from a new threat in the human world that no one else is aware of. Sulley initially doubts Randall but as he sees the evidence, he decides to help Randall. They then team up and use their different skills - Sulley's big and strong nature and Randall's sneaky and intelligent ways - to overcome the threat and in the process, their relationship changes for the better.
It's also because their personalities are so different yet complementary. Sulley is big and strong while Mike is small and smart. Fanfiction writers can play with these characteristics in various ways. For example, they can create stories where Mike's ideas and Sulley's ability to execute them lead to amazing results. This contrast makes for interesting and engaging stories.
One good example could be fanfictions that focus on their adventures outside of work. For instance, a story where they go on a trip to a new, uncharted part of the monster world. Another might be ones that explore their friendship during their childhoods, like how they first met at monster school.
There's also a fanfic called 'Sulley and the Mysterious OC'. In this one, a mysterious OC shows up at Monster Inc and Sulley is the first to notice something strange about them. It has a lot of mystery elements and is quite engaging. It delves into the idea of how the monsters at Monster Inc react to an unknown entity in their midst.
In a different take, Sulley and Randall could be partners in a secret experiment within Monsters Inc. They might be working on a new way to collect energy from kids without scaring them. As they work closely together, they discover that they have a lot in common when it comes to their love for the monster world and their hopes for its future. This shared passion could lead to a deeper bond between them, different from the adversarial relationship in the movie.