One possible plot is that the guy in the van is actually under the control of a more powerful villain. The anime girl, who might be a key figure in the anime's lore, is kidnapped to be used as a bargaining chip. However, during her captivity, she befriends a small creature or another captive in the van. Together, they come up with a plan to escape and expose the real villain behind the kidnapping.
She may start by trying to figure out who the kidnapper is and what his motives are. If she has any special abilities or skills, she would be thinking about how to use them to her advantage. For example, if she has telepathic powers, she could try to send a distress signal to her friends or family. Also, she might try to gain the kidnapper's trust in order to find a moment to escape.
Maybe the guy in the van has a personal vendetta against Sango. He might be someone from her past that she wronged accidentally. In the fanfiction, Sango could use her combat skills to try and escape the van when the kidnapper least expects it.
She could be held hostage in an abandoned building. The kidnapper might demand a ransom from her friends in the anime. Her friends would then have to figure out how to get the money and rescue her without getting caught by the kidnapper's traps.
Perhaps the anime girl was kidnapped because she holds a special key or knowledge that the military guards want. She could be from a world where anime rules apply, and her knowledge of that world's magic or technology is what attracted the military's attention. She will then go through a series of adventures within the military compound, making friends with some of the inmates (if there are any) and planning her great escape.
Perhaps the obsessed guy has a change of heart. He realizes his actions are wrong and lets the girl go. But this ending often comes with a complex set of emotions and consequences for both characters as they try to make sense of what has happened.
One possible motive could be for experimentation. They might believe the anime girl has unique abilities that could be harnessed for military purposes, such as superhuman strength or special psychic powers.
In fanfiction, if an anime girl is kidnapped by the military, it could lead to a story of rescue. Maybe her friends or some heroic characters will start a mission to save her. They might have to face various challenges set by the military, like security systems and trained soldiers.
The anime girl might be used as a bargaining chip. If there are different factions in the military or if there is some sort of political turmoil, the group that kidnapped her could use her to gain an advantage. For example, they could threaten to harm her if their demands are not met.
One example could be a fanfiction where a mysterious guy kidnaps a character from a popular TV show. For instance, in a fanfic based on a superhero series, a villainous guy might kidnap the superhero's sidekick to lure the hero into a trap. This creates a lot of drama and tension in the story as the hero then has to figure out how to rescue their friend.