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.
It could mean a fan - created story where Hermione (presumably from the Harry Potter series) is in a state of being 'broken', perhaps emotionally, psychologically or physically. This might be explored in a non - canon way in the fanfiction.
I'm sorry, I can't directly recommend specific 'hermione is broken fanfiction' as there are countless fanfiction works out there and it's hard to single out ones with this exact theme. However, you can search on popular fanfiction websites like Archive of Our Own (AO3) or FanFiction.net using relevant keywords like 'Hermione broken' to find such stories.
Snape could offer Hermione a book to distract her. Knowing her love for knowledge, a rare and ancient book about magic could draw her attention away from whatever is breaking her. It would be his way of saying that there are other things to focus on and that she can find solace in learning.
Snape could also share some of his own experiences of being an outcast and misunderstood. He might tell Hermione that he too has faced hardships and that it is possible to rise above them. For example, 'I have been judged wrongly all my life, Miss Granger. Yet here I am, still standing. You are far stronger than you think.' This would give Hermione a new perspective and comfort her.
Maybe Hermione has a morning encounter with an unexpected character, like a centaur who comes to her with a warning about something that will happen during the day. This sets off a chain of events where she has to use her wits and knowledge to prepare for it while the morning unfolds around her. It could involve her running around the castle, gathering resources and allies all before breakfast.
I'm not sure about a specific 'Morning has broken' Hermione fanfiction off the top of my head. You could try searching on popular fanfiction websites like Fanfiction.net or Archive of Our Own. Type in the keywords 'Morning has broken' and 'Hermione' and you might find some interesting reads.
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.
He may show a rare moment of kindness. Given his own past traumas and experiences, he might empathize with Hermione on some level. He could offer her some words of wisdom or even some form of magical assistance to help her get better.
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.