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.
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.
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.
There are many fanfic platforms where you can find 'Percy Saves Artemis' fanfics. For example, FanFiction.net. You can simply search for the specific tag and browse through the available stories. Some might be action - packed with Percy using his demigod powers in creative ways to rescue Artemis.
One common plot element is Percy facing some sort of powerful enemy or threat that has captured Artemis. This could be a new, never - before - seen monster in the Percy Jackson universe.
Well, in many fanfictions, Naruto might use his ninja skills. He could use his speed to reach Artemis quickly if she's in danger, like if she's being attacked by some powerful enemy. His shadow clone jutsu could also be useful to distract the foes while he rescues her.
I don't know for sure as I haven't read this particular fanfiction, but usually in fanfiction, Percy could be a character from a popular book, movie or TV series.