He could also become withdrawn and depressed. Percy and Annabeth have a very strong bond, and her death would leave a huge void in his life. He might isolate himself from his friends and family, lost in his grief and memories of her.
Rebuilding is also a theme. After Percy's death, the world around the characters might be in chaos. So, in many fanfictions, they have to work towards rebuilding what was lost, whether it's a physical place or the sense of hope that Percy once brought.
Percy might become more independent. Without his mom's presence, he has to rely more on himself. He could start to take on more leadership roles within the demigod community. He also may develop a darker side to his personality, as the pain of his mom's death lingers. However, through his experiences and the support of his friends, he gradually learns to balance this new, harsher side with his original kind - hearted nature.
In this fanfiction, Percy might sacrifice himself in a grand battle. He could be facing a powerful enemy that was about to strike Zoe. Percy, being the heroic type, jumps in front of Zoe at the last moment. His last thoughts could be of his friends and all the adventures he had. Zoe, in turn, is left with a deep sense of guilt and sorrow, vowing to carry on Percy's legacy. She might become even more determined to fight for the cause they both believed in, all while mourning the loss of her dear friend.
In this kind of fanfiction, it's often a very tragic and heroic concept. Percy sacrificing himself to save the seven would be a huge shock to the other characters. It might lead to a lot of grief and also a new sense of purpose for the remaining seven. They would have to carry on with their mission while also dealing with the loss of Percy, which could add a lot of depth to their character development.
In this type of fanfiction, it's a really interesting concept. One possible scenario could be that Percy's death is a heroic sacrifice. Maybe he gives his life to save the world from an even greater threat than before. And when he becomes a god, he might use his new powers to bring about a new era of peace among the gods and demigods. His transformation could also mean changes in his relationships. For example, his friends might now have to view him in a different light, as a divine being rather than just a fellow demigod.
Annabeth is often the one to save Percy. She's smart and resourceful. For example, she might use her knowledge of architecture to find a way out of a collapsing building that Percy is trapped in. Or she could use her strategic thinking to outwit a monster that has Percy at its mercy.
Percy would be completely devastated. He might go into a state of shock at first, unable to believe that Annabeth is really gone. Then he could become filled with rage, vowing to take revenge on whoever or whatever was responsible for her death.
A possible plot in such a fanfic could be Percy trying to bring Sally back from the dead. He could go on a dangerous and forbidden quest, defying the gods and the natural order. This would put him at odds with many, but his love for his mother is so strong. He might encounter dark magic or make deals with shadowy figures in his desperation, all while his friends are worried about him losing himself completely in this quest.
One popular 'Percy Dies' fanfiction is 'The Aftermath of Percy's Demise' on FanFiction.net. It explores how the other characters deal with his death and the changes it brings to their world.