He might meet other inter - galactic beings. For example, some sort of space - faring demigods from a far - off galaxy. Or he could encounter powerful entities that are the rulers of other planets.
Percy might be very confused at first. He would wonder why his mother, who has always been there for him, suddenly left. He could start to question if he did something wrong. In some fanfics, he may go into a state of denial, not wanting to believe that she's really gone.
In a 'Percy Jackson leaves earth' fanfic, he might end up in a whole new realm of gods and monsters. Maybe he discovers a parallel universe where the rules of the Greek gods are different. He could encounter new versions of his friends or enemies and have to learn new powers to survive.
Another reason might be that she is forced to leave. There could be a magical or divine force at play. Maybe a god or goddess, who has some grudge against Percy or his father Poseidon, manipulates the situation so that Sally has no choice but to abandon Percy. This would add a lot of drama and conflict to the fanfic.
There could be a fanfic where Percy leaves because he feels out of place after all the battles. He decides to start a new life away from the demigod world. In the fanfic, he tries to adapt to a normal human life but finds it difficult as his demigod instincts keep getting in the way.
Another reason could be to give Percy a chance to find himself. In the original stories, he is often defined by his role as a demigod and his relationships. When he leaves, he can start to figure out who he is without those labels, and authors can use this to delve deeper into his personality and motives.
He might go on a solo adventure to discover more about his powers. He could encounter new mythical creatures that he hadn't seen around the camp. Maybe he'll meet some other demigods who are on the run or have their own secret quests.
One great 'Percy Jackson' fanfiction where he leaves could be about him leaving Camp Half - Blood to explore the human world on his own. In this kind of story, he might face challenges that are different from the ones in the camp, like dealing with modern technology without the help of his demigod friends. It could also show his growth as he discovers new aspects of himself.
You can try fanfiction.net. It has a large collection of fanfics from various fandoms, including Percy Jackson. Just use the search function and type in 'Percy Jackson Leaves' and it should show you relevant stories.
Yes, in some Percy Jackson fanfics, he could be depicted as a Titan. Fanfic writers often take creative liberties and might come up with unique storylines where Percy has Titan - like qualities or is even reimagined as a Titan for the sake of an interesting plot twist.