Annabeth would be very shaken up. After the initial shock, she would assess the situation calmly. If Percy is unconscious, she would try to find a way to wake him up. She might talk to him, recalling their memories together, hoping it would reach him on some level. And she would be very protective of him while he's injured, not allowing any further harm to come to him. She would also feel guilty, thinking that if she were stronger or more careful, Percy wouldn't have had to protect her and get hurt in the first place.
She might realize it when she sees Percy's reaction to her actions. For example, if Percy looks at her with such disappointment and hurt in his eyes, it could be a wake - up call for Annabeth. That look could make her see how much she has damaged their relationship.
Annabeth would probably be really frustrated. She might try to jog Percy's memory by showing him things that are important to their relationship, like the Camp Half - Blood necklace she gave him or their shared adventures. She's a smart and determined character, so she won't give up easily.
Kronos might have some minions do the dirty work for him. They could be disguised as normal people and surround Annabeth when she's alone. Then they could overpower her and take her to Kronos. It's also possible that he uses some sort of magic or spell to immobilize her first and then kidnap her.
Well, in some fanfictions, Percy might reject Annabeth because of misunderstandings. Maybe he misinterprets something she says or does, leading to him pushing her away.
In some fanfictions, the world - building or the plot might force a rift between them. If the story is set in a situation where resources are scarce and they have different ways of handling it. Hermione's more logical and rule - based approach might clash with Annabeth's more instinct - based approach, leading to Hermione hating her.
It could be that the fanfiction plots are so convoluted. For example, the writer might create some really out - of - character situations for Percy and Annabeth. If Percy is constantly put in scenarios where he's made to be at odds with Annabeth in ways that don't feel true to the original series, it could give the impression that he hates her in the fanfiction.
When Annabeth is mad, Percy will likely try to make it up to her. He might start doing all kinds of things like bringing her favorite foods, trying to help her with her projects. But Annabeth might not be so easily swayed. She'll be looking for a real apology and for Percy to show that he's learned his lesson. So the relationship becomes a bit of a power struggle, with Percy trying to regain her favor and Annabeth deciding whether he's worthy of it.
Annabeth could also try to solve the problem that's making Percy cry. If it's related to a quest or a danger, she'll start thinking of ways to fix it. In some fanfictions, she might say 'Don't worry, we'll figure this out together.' and then start making a plan.