Annabeth might find him. She's always been close to Percy and they often go on adventures together. So it's likely that she'd be the one to come across him when he faints.
In certain fanfiction stories, Ash could faint as a result of a psychological shock. Imagine if he discovers that one of his beloved Pokemon has been mind - controlled by an evil organization. The sheer horror and disbelief could be so overwhelming that he faints. Additionally, he might be caught in a powerful psychic attack from a very strong psychic - type Pokemon that not only weakens his physical state but also his mental state, leading to his fainting.
I'm not sure specifically what that 'beckett faints fanfic' is about without reading it. It could be a fan - created story where a character named Beckett faints and then various things happen around that event, like other characters' reactions, or the events leading up to and following the fainting.
His friends like Pikachu would be very worried. Pikachu would probably stay by Ash's side, trying to use its electric shocks gently to revive him. Misty might scold Ash for being so reckless but also show concern by getting water to cool him down. Brock would immediately start checking Ash's vital signs and try to figure out what went wrong.
Another scenario could be that Data faints as a result of overloading his emotional subroutines. He's been trying to experience emotions more deeply and it becomes too much for his current programming. This would open up a story about how the crew helps him manage and understand his emotions better, and how they deal with this new vulnerability of Data.
One interesting 'clary faints fanfic' could be about her fainting during a battle due to overexertion. Maybe she's been fighting demons for hours and her body just gives out. The other characters then have to protect her while she's unconscious.
There's 'When Snape Faints in the Potions Classroom'. This fanfic focuses on the reactions of the students when Snape faints while teaching a potions class. Some students are scared, some are curious, and it's interesting to see how they handle the situation without an adult immediately available.
Perhaps in a fanfiction set during the time of the Triwizard Tournament. Snape faints because he has been secretly working to protect Harry Potter from a hidden threat related to the tournament. He has been using a lot of magic and energy to keep an eye on Harry without him knowing. One day, after a particularly close call, the stress and magic depletion make him faint right in the middle of the Great Hall.