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.
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 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.
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.
Perhaps they love the sense of community that comes with fanfiction. There are often groups of fans who write, read, and discuss fanfiction, and Paige and Emily might enjoy being part of this community, sharing their thoughts and ideas about the stories they love.
Overcoming obstacles is another theme. It could be things like dealing with a rival or facing difficulties within their families. In these stories, Paige and Emily rely on each other to get through tough situations and their relationship is strengthened as a result.
One common theme is friendship. Their bond as friends is often explored deeply. Another is growth, like how they grow as individuals within their relationship. Also, loyalty is a big theme as they are often shown being loyal to each other in fanfiction.
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.