A possible kidnapper could be a new character introduced in the fanfiction who has a dark obsession with Emily. This person might have been watching her from afar, learning her routines, and waiting for the perfect opportunity to kidnap her. They could be motivated by a desire to have Emily all to themselves, or perhaps they believe that Emily has some special power or knowledge that they want to extract from her.
I'm not sure specifically as this title seems inappropriate and I don't have access to such fanfiction. Fanfiction often takes characters from a source material like 'Pretty Little Liars' (assuming PLL refers to that) and creates new stories, but this title contains inappropriate language.
In some PLL Emily kidnapped fanfiction, the story could be centered around a misunderstanding. Let's say there's a new group in town that mistakes Emily for someone else who they think has wronged them. So they kidnap her. As she's held captive, Emily tries to convince them of their mistake. Meanwhile, her friends are worried sick and are trying to find her. They search through her recent activities, her contacts, and any strange happenings in town. They might also get some help from Caleb or Toby, who have their own skills in finding people. Emily, on her part, might find a way to communicate with the outside world, like using a hidden phone or leaving signs in the room where she's being held.
One common theme is betrayal. For example, in some fanfictions, Alison might betray Emily's trust, which causes emotional pain. Another theme is dealing with past traumas. Since both characters have had a lot going on in the show, fanfictions often explore how they handle those past events resurfacing and hurting them again.
A theme that can't be ignored is acceptance. In the PLL world, not everything is as it seems, and the reader may have to deal with things like not being accepted by others in Rosewood at first. Emily helps the reader through this, and it becomes a journey of both of them learning to accept themselves and each other. Also, the theme of family, whether it's the reader's family situation or Emily's complex family relationships, often plays a role in these fanfics.
Another place could be near the old abandoned houses in Rosewood. Fanfictions often use such spooky locations. They could be lured there and get hurt while trying to escape from a trap set by an enemy.
One great source could be fanfiction.net. There are often a variety of stories featuring Alison and Emily in difficult or 'hurt' scenarios. Just search for 'PLL Alison Emily hurt' on the site, and you'll be presented with multiple options to choose from.
They might rely on each other for support. Emily could use her athletic skills to get them out of dangerous situations and then they would tend to each other's wounds.
One popular 'pll Emily x reader fanfic' might be 'Emily's Hidden Feelings'. It delves deep into the relationship between Emily and the reader. It has great character development and really captures the essence of the Pretty Little Liars world.