Another plot could be that Snape assigns the student to clean his office during detention. While cleaning, the student finds old parchments and journals that give insights into Snape's past, especially his time as a student at Hogwarts. The student becomes more empathetic towards Snape after learning about his difficult past and tries to befriend him, which Snape initially resists but gradually warms up to.
One plot idea could be that during detention, Snape discovers Hermione's hidden talent for potion-making that even he hadn't expected. He starts to see her in a new light, not just as an over - achieving Gryffindor. Another idea is that they get trapped in the detention room due to a spell gone wrong, and they have to work together to get out, which leads to a grudging respect between them. And perhaps Hermione finds an old diary in the detention room that has some secrets about Snape's past, which she uses to understand him better.
Some fanfictions have the idea that while in detention, Harry and Snape are magically bound to work together on a special potion. This potion has the power to reveal hidden secrets. As they work on it, they start to share their own secrets, like Snape's unrequited love for Lily and Harry's fears about Voldemort. It's a really interesting way to develop their relationship.
One interesting scenario could be that during detention, Snape makes Harry clean all the potion bottles in the dungeon while lecturing him about the importance of precision in potions. Harry, in turn, discovers an old, forgotten potion recipe among the bottles and Snape is grudgingly impressed.
Maybe in the fanfic, Snape gives Hermione detention for accidentally disrupting his class. But instead of a typical punishment, he assigns her to help him organize his personal library of dark arts books. As they work together, Hermione begins to understand Snape's complex past and Snape starts to see Hermione in a new light, beyond just being a know - it - all Gryffindor.
Perhaps in the fanfiction, Snape assigns Harry to clean all the old potion vials in the storage room during detention. While doing so, Harry discovers an old diary that seems to hold secrets about Snape's past at Hogwarts, which then leads to a series of revelations and a change in their relationship.
One idea could be exploring Snape's childhood before Hogwarts. Maybe he had a secret friendship with a Muggle that no one knew about. This could add depth to his character and explain some of his later actions.
Another interesting plot could be a backstory about how Snape first got involved with Voldemort. Maybe it was out of a thirst for power initially, but then his views changed over time. This could be delved into in great detail, showing his transformation from a potential dark wizard follower to a hero in the fight against Voldemort.
One idea could be that during detention, Hermione discovers a hidden magical artifact in the classroom. This leads to an adventure where she has to figure out its purpose and keep it safe from those who might misuse it.
Well, perhaps Snape sets them to clean the potions classroom. Draco tries to boss Harry around at first, but Harry refuses to be pushed. As they clean, they accidentally knock over a vial that releases a magical mist. The mist makes them relive some of their worst memories involving each other. This forces them to understand each other's perspectives better and by the end of detention, there's a less hostile air between them.
One idea could be exploring Snape's early days at Hogwarts as a student. Maybe his first encounter with Lily Evans and how that shaped his future. Another could be a what - if scenario where Snape decides to fully side with Voldemort in a different way, changing the course of the wizarding war. Or perhaps a story about Snape's relationship with his fellow Death Eaters and how he really felt about them.