In many fanfictions, Kakashi might save Naruto from suicide by using his Sharingan. He could see Naruto's inner turmoil and use his jutsu to snap Naruto out of his dark thoughts. For example, he might use a genjutsu to show Naruto all the people who care about him and how much he means to the village.
Another way Kakashi could save Naruto is by physically intervening. If Naruto was about to do something harmful to himself, Kakashi's ninja skills would allow him to quickly stop Naruto. Then he could take Naruto to a safe place, like the Hokage Monument where they could have a long talk about Naruto's problems and how to face them.
In some fanfictions, it could be due to a special jutsu gone wrong. Maybe a jutsu that Kakashi was using to transfer some of his chakra to Naruto for a mission accidentally transferred his Sharingan power as well.
The moment when Kakashi actually reaches Naruto and stops him from harming himself is crucial. He could use his speed and strength to grab Naruto's hands if he was about to use a weapon on himself. Kakashi's presence alone at that moment can be a shock to Naruto, making him pause and re - consider.
Naruto might also try to find alternative ways to gain strength. He could explore the forest around the village to find new training areas or discover new chakra - related phenomena. He has a curious nature, and this could lead him to stumble upon something that gives him an edge in his training, like a hidden hot spring that has special chakra - enhancing properties.
Well, it could be that Naruto has developed a new and powerful form in the fanfiction. With this form, he emits an intense chakra that scares off the Cloud attackers who are after Hinata. His speed and strength in this new form are so great that he can easily reach Hinata and get her to safety before the Cloud ninjas can react.
Well, in many fanfictions, Naruto might use his signature jutsus like the Rasengan. He could sense the danger the woman is in using his enhanced ninja senses and then quickly dash in to counter Rizevim's attack with his powerful moves, overpowering Rizevim and rescuing the woman.
Well, Naruto is known for his quick thinking. So perhaps he quickly assesses the situation and uses the surrounding environment to his advantage. For example, if there's a water source nearby, he could use his water jutsu skills (if he has them in that fanfiction) to counter the fireball and save Ami. Or he might even use his body as a shield if it comes down to it, relying on his Uzumaki durability.
In some fanfictions, Naruto might use his new jutsu that he's developed through intense training. He could overpower Kabuto with his Rasengan variations, like the Big Ball Rasengan, and rescue Tsunade while Kabuto is distracted by the powerful attack.
In some fanfictions, Naruto might use his new jutsu skills that he's developed in secret training. He could surprise Neji with a powerful Rasengan variant, overpowering him and rescuing Hinata.
In the fanfiction, Naruto might use his shadow clone jutsu. He could create multiple clones to surround the kidnappers and disorient them. Then, while they are distracted, he could swoop in and rescue Moegei.
Well, in some fanfictions, Fu might use her unique jutsu skills. For example, she could create a powerful barrier to protect Naruto from Sakura if Sakura is somehow being controlled or acting aggressively. Fu's ability to manipulate nature energy could also play a role. She might use it to disorient Sakura or make her lose her focus on Naruto.