Moments before his death, Rengoku tells Tanjiro that he believes in the young demon slayer's sister, Nezuko, and her ability to retain her humanity despite being a demon. Rengoku, unlike many of the other Hashira demon slayers, believed Nezuko could be saved.
At its core, "Demon Slayer" is about Tanjiro's love and dedication to the only family member he has left — his sister — and his quest to turn her back into a human. The uniqueness of Tanjiro and Nezuko's situation is established in the first episode, when Hashira Giyu Tomioka tries to kill Nezuko moments after Tanjiro discovers his family was slaughtered. Nezuko quickly proves she's an exception to every rule the Demon Slayer Corps knew about demons when she defends her brother.
Despite her loyalty to humans and relative lack of bloodthirstiness, the rest of the Hashira aren't convinced of her goodness when they meet her during Season 1. But throughout the first season and especially in the "Mugen Train" film, Nezuko hones her own fighting skills and helps the trio slay demons. In the film, Nezuko is also key to getting Tanjiro to wake up from Enmu's dream-induced spell.
Demon slayers are known for their courage, strength, loyalty to humanity and their dedication to protecting the world from demons. Nezuko may not be human, but she's become a demon slayer in her own right. Rengoku's belief in the young girl, meanwhile, makes his death all the more heartbreaking.