It could also be that Whitney is separated from her Pokemon. For example, there could be some sort of Pokemon - stealing gang in the story. They manage to take her Pokemon away from her. She loves her Pokemon like family, and the thought of being without them makes her break down in tears.
A simple emotional trigger could be homesickness. Whitney might be far away from her hometown in the Pokemon world. She misses her family, friends, and the familiar places. This loneliness and longing can lead to her crying.
Perhaps the real reason behind the kidnapping has to do with a secret Pokemon that Whitney has. It could be a legendary Pokemon that she's protecting, and the kidnappers want to use it for their own evil purposes. And then, when the rescuers think they've found Whitney, it turns out to be a decoy set up by the kidnappers.
Suppose James enters a Pokemon beauty contest for his favorite Pokemon. But due to some underhanded tactics by other contestants, his Pokemon loses. James, who had put so much hope and effort into it, starts crying as he feels he let his Pokemon down.
Maybe Wendy is crying because her favorite Pokemon got hurt in the fanfiction. It's really sad when a beloved Pokemon is in pain.
One possible reason could be her separation from her Pokemon. In the Pokemon world, the bond between trainers and their Pokemon is extremely strong. If Lillie were to be separated from a beloved Pokemon, perhaps due to some unforeseen circumstances like it being captured by a villainous team, she would be heartbroken and cry. Another reason might be related to her family. Maybe there are secrets within her family that are revealed in the fanfiction, and these revelations are so overwhelming that she can't help but cry.
One possible reason could be that Pikachu is separated from Ash. In many fanfictions, their bond is so strong that being apart would be extremely distressing for Pikachu, leading it to cry.
I haven't actually read this fanfic, but generally, a story about 'kidnapping Whitney' in the Pokemon universe could be really dark. It might explore themes like danger in the Pokemon world that's usually seen as a rather safe and friendly place for trainers. Maybe it's a way to create high - stakes drama.
One possible fanfiction could be that James loses his beloved Weezing in a battle. He has had Weezing since he was a child, and it was like his only true friend in Team Rocket. So when it faints and doesn't get up, he starts crying. He realizes how cruel the world of Pokemon battles can be and has a moment of self - reflection about his life in Team Rocket.
One possible plot could be that Freebat has some sort of misunderstanding with Billy. Maybe Freebat accidentally breaks Billy's favorite item, which makes Billy start crying. Then the fanfiction could explore how they resolve this conflict, perhaps through a series of apologies and reconciliations.
One possible plot could be that the baby boy is in a new and strange environment. Maybe he's been adopted into a family in a fanfiction world. He's confused because the new family has different customs or appearances than what he's used to. His crying could be a way to express his discomfort and fear. For example, if it's a fantasy fanfiction, the family could be elves or some other non - human species.