Maybe it was a result of a botched spell during a duel. In the wizarding world, duels can go wrong very quickly. If Hermione was facing a powerful opponent, perhaps one of their spells backfired on her in a way that left her broken, both physically and possibly emotionally.
One possible reason could be that she was attacked by some dark creatures while on a solo adventure in the Forbidden Forest. The forest is full of dangers, and Hermione, being brave and curious, might have ventured too deep and got injured by a creature like a werewolf or a giant spider.
It could also be related to some sort of time - turner malfunction. We know Hermione used a time - turner before. If in the fanfiction she was using it again and something went wrong with it, it could have sent her through time and space in a chaotic way, causing her to be in a broken state when she finally landed in Snape's path.
One possible reason could be the stress from her studies. Hermione is always under a great deal of pressure to excel academically. Maybe she reached a breaking point due to the overwhelming workload. Another reason might be some kind of conflict with her friends. For example, if she had a big fight with Harry or Ron over something serious, it could leave her feeling broken.
Perhaps she's being bullied. In the wizarding world, there could be other students who pick on her because she's a 'Mudblood'. This could be really distressing for Hermione, and when Snape finds her crying, he might be conflicted between his general dislike for Gryffindors and his sense of justice.
One possible reason could be a misunderstanding. Maybe Hermione thought Snape was involved in some dark plot against her friends. In the wizarding world, there are often secrets and deceptions, and if she got some false information, it could lead her to take such drastic action.
It could be a failed experiment in potions class. Hermione is always eager to try new things in potions, and perhaps this time it backfired, causing her some harm. And Snape would be the one to find her because it's his class.
Snape might be suspicious at first. He might think it's some sort of trick or part of a bigger plot. However, as he observes Hermione more closely and realizes the genuineness of her situation, his attitude could gradually change to one of reluctant assistance. He might even offer some words of wisdom, albeit in his typical sarcastic way, to help Hermione regain her strength.
Hermione is also very confident in her knowledge. Snape is an expert in Potions, but Hermione is no slouch either. So, when Snape tries to undermine her in Potions class, she might respond with sarcasm. For example, if Snape corrects her in a way that she thinks is wrong, she could say 'Of course, Professor, your infinite wisdom must be right' in a sarcastic tone.
In fanfiction, sometimes authors like to break boundaries and explore 'what - if' scenarios. For the 'Snape cheats on Hermione' idea, it could be a way to create drama and conflict. They might be interested in exploring the emotional turmoil it would cause for Hermione, or how it could change the relationships within the wizarding world they've created in their story. It could also be a way to subvert the typical hero - heroine relationships we see in the original series.
One possible reason could be a powerful spell gone wrong. Maybe she was caught in the crossfire of a dark magic spell that Snape was either trying to counter or was involved in accidentally. Another reason might be extreme emotional shock. For instance, if she discovered some dark secret about Snape that was so overwhelming it sent her into a catatonic state.
One possible reason could be that Snape sees Hermione's value as a brilliant student. He might recognize her potential and not want it to be wasted just because of her dad's actions or situation. Maybe he has a sense of justice deep down, despite his often cold exterior.
One possible reason could be that Snape has shown unexpected kindness to Hermione in the fanfiction. Maybe he has protected her from some danger secretly, which makes her feel she can rely on him and thus feel safe.