Nara Shikamaru had been just another sacrifice for Jashin. Konoha mourned the loss as a whole. Chouji and Ino became more distant after that battle, as their friends could attest. And yet his plan had been so good. It was thought out perfectly; Hidan had merely surpassed him in strength and blocked its execution.
Uzumaki Naruto defeated Kakuzu using his wind-based rasengan, but his company left him to die on the hard earth. A spark of life still existed in him, and after everyone had left, his one beating heart pushed him to stand and exit the stage. His pride was damaged; the next generation had surpassed him, and he was powerful. Nonetheless, he was alive.
Hidan couldn't find Kakuzu after taking care of the weakling who'd dared to contradict his god's judgment. He started off on his own and looked for him for the duration of a month before giving up. It was such a prize to lose, the privilege of throwing caution in the wind during battle because Kakuzu could sew him together at will. That prize was the most substantial reason for his joining the Akatsuki in the first place. Hidan never returned to take orders from Pein again.
The two went their separate ways without knowing each other's location. Hidan fought in the ensuing war alone. Kakuzu stayed out of it entirely. While Hidan didn't want to forgo the opportunity to witness and participate in the creation of such a beautiful array of deaths, Kakuzu was tired of fighting. Reflecting on his life made him feel like an old man, and he was exhausted. Over the course of the next three years, he only killed four ninja, and those died to serve as unwilling organ donors.
The war ended with Madara's defeat. The Akatsuki faded away into the pages of history. Hidan didn't feel anything for its passing; he simply continued on and fulfilled his divine mission. Once again, he was a rogue ninja, snatching his food from the earth or striking down running targets to cook and eat. He usually chose the latter; animal meat fed his stamina better than anything else. His god was the only being around to keep him company, but he didn't answer Hidan's prayers out loud. His days fell into a repetitive routine, and he quickly grew bored of them and languished in the monotony of his immortal life. He didn't usually come across travelers on his path, and so his only source of entertainment was, with only the rare exception, thoroughly mutilating his own body.
Kakuzu, contrarily, took a long vacation from the rogue lifestyle. He put his reserves of strength to the side and relaxed in the way a typical old man should have been allowed to. He shed his identity and, using a semi-permanent form of transformation jutsu he'd discovered, assumed a new face and role in life. He knew a woman, a fairly pretty brown-eyed dame, and settled down with her but refused to be married. His avarice eventually flared up again, however, and he started a scheme to swindle his neighbors out of their money. It proved effective.
Once Kakuzu's girlfriend learned about his dishonesty, she confronted him about it and they got into a fight. Kakuzu's temper succeeded his desire for stability and he murdered her in a fit of blind rage. He regretted it afterwards. She'd been a nice thing to have, and he was subsequently forced to leave the town with all the money he'd stolen.
Hidan came across Kakuzu in the forests surrounding Konohagakure four months after this happened. It was the first time the two had met since they'd fought Hatake Kakashi and his squad.
A/N: Odd place to end the chapter, I know. It's neither conclusive nor a cliffhanger. Next chapter will include dialogue.