In the fanfiction, Artemis might use her divine powers. Maybe she creates a distraction so that Percy can escape from Gabe. For example, she could make a sudden bright light or a loud noise that confuses Gabe, giving Percy the chance to run away.
Maybe Artemis sees Percy's potential. Percy has shown great courage and skill in other situations, and Artemis might recognize that he could be an important asset in the future battles against the forces of evil. So, she decides to save him from Gabe, who is a nuisance and a threat to Percy.
The Hunters of Artemis are very likely to show up. They are Artemis's loyal followers and would surely be involved in the search for their mistress. Annabeth could also be there. She's Percy's friend and has great wisdom, which could be useful in devising a plan to save Artemis. Grover might be another character. His ability to sense things could help in tracking Artemis or finding clues about her whereabouts.
One possible plot could be that Artemis is captured by some powerful ancient enemy, like a primordial being. Percy, with his skills and courage, embarks on a quest to find her. He might face various challenges and monsters along the way. Maybe he has to solve some riddles related to the moon, as it's Artemis's domain. Finally, he locates Artemis and uses his water powers in a creative way to defeat the captor and free her.
I haven't actually read this specific fanfiction, so I can't summarize the exact plot. But generally, it might involve Percy being in a very dark and suicidal state, and Artemis somehow intervenes. Maybe she uses her powers or her wisdom to show Percy that there are reasons to keep living, like the importance of his friends, his potential to do great things in the future, or the value of his own life in the grand scheme of their fictional world.
It could be that Percy has been ostracized or misunderstood by the people he cares about. If his actions were misinterpreted and he was made to feel like an outcast, that might have led to his suicidal thoughts. Also, he might be suffering from some kind of prophecy or fate that seems inescapable, and he thinks death is the only way out.
In many fanfictions, the hunters would first assess the situation. If Percy is being held captive by Gabe, they may send in a stealthy member to find Percy's exact location. Once they know where he is, they would launch a coordinated attack. The hunters are known for their teamwork. They could surround Gabe's place, and some might engage Gabe directly while others free Percy. Their connection to nature might also give them an edge, like using the environment to their advantage during the rescue.
One possible scenario is that the hunters disguise themselves as normal people and approach Gabe's place. When Gabe least expects it, they reveal their true identities and take him by surprise, saving Percy. Another could be that they use their tracking skills to find Percy's location even if Gabe has hidden him well.
Well, it could be that in the fanfiction, Percy gets into fights with Gabe over protecting his mother. Gabe, being the brute he is, might use a weapon or his fists, and Percy ends up with scars as a result. For example, he could try to stop Gabe from hitting his mother, and Gabe turns on him, causing injury that leaves scars.
Annabeth is quite popular. Since she has a relationship with Percy in the original series, in fanfiction related to Percy and Artemis, she can be a source of conflict or support. For example, she might be jealous of the time Percy spends with Artemis. Another popular character is Thalia. Her connection to Artemis as a member of the Hunters makes her an important figure. She can add more depth to the stories, especially when it comes to the dynamics between the Hunters and Percy. And then there's Grover. His loyalty to Percy and his unique abilities as a satyr can bring a different flavor to the fanfiction. He might be the one who tries to mediate between Percy and those who are skeptical of his association with Artemis.