In some fanfictions, Konan might use her origami techniques in a highly lethal way. Maybe she creates a large number of explosive paper bombs and traps Obito in a confined space, detonating them all at once to overpower his defenses and kill him.
It might be for the greater good. If Obito's actions in the fanfic are leading to destruction on a large scale, Konan, being a protector of sorts, decides to take him out to save the world or at least her part of it.
In an 'Obito kills Kakashi' fanfiction, it could start with a long - standing grudge. Maybe Obito discovers some new information that he believes Kakashi has been hiding from him all these years. This enrages him so much that he decides to take revenge and kills Kakashi in a fit of rage during a battle.
Well, Naruto has a lot of unique abilities. He could enter Sage Mode and use his enhanced perception to outmaneuver Obito. Konan, on the other hand, is a very skilled fighter herself. But against Obito's Sharingan and his space - time ninjutsu, she might be at a disadvantage. Naruto could use his talk - no - jutsu to make Obito realize the error of his ways and stop attacking Konan. This would be a very Naruto - like way to end the confrontation.
Some fans would be really shocked and sad. Kakashi is a very popular character, and his death at the hands of Obito would be a huge blow to many. They might feel angry towards the author for creating such a tragic scenario.
Naruto's character could develop a deeper sense of responsibility. Saving Konan from Obito would show that he is not only protecting his close friends from Konoha but also those from other villages. This would expand his view of what it means to be a hero.
In some Konan Lemon fanfics, Konan might be portrayed as a more vulnerable yet passionate character. Since 'lemon' often involves romantic or sensual elements, she could be shown as having a softer side when it comes to relationships, different from her usually tough and mysterious self in the original Naruto series.
In the fanfiction, Konan may start to see the world through Naruto's eyes. Naruto has a very positive and hopeful view of the ninja world despite all the hardships he has faced. This could influence Konan to question some of her own beliefs and actions, leading to a significant change in her character.
Naruto could be one of his allies. Naruto has this knack for seeing the good in people and would probably be willing to give Obito a chance to redeem himself. Also, Sakura, with her skills as a medic - ninja, could be an ally. She might help heal Obito if he was injured during the war and see the potential in him to be a force for good.