Summary
The following contains major spoilers for the Demon Slayer: Kimetsu no Yaiba manga, by Koyoharu Gotouge, available in English through Viz Media.
Yoriichi Tsugikuni is one of the most important and mysterious characters in Demon Slayer's lore. The creator of Sun-Breathing, the original and most powerful of all Breathing Styles, Yoriichi is the indisputable strongest when it comes to Demon Slayers.
Though he died ages before the series' present day, his Sun-Breathing lives on thanks to Tanjiro, who now wields the most powerful Breathing Style and bears a striking resemblance to the Original Sun-Breather. Yoriichi, like many in a world filled with demons, lived a tragic life, but his relationship with the Kamado family provides a surprising twist on one of Demon Slayer's most often asked questions: is Tanjiro related to Yoriichi?
Who Is Yoriichi Tsugikuni in Demon Slayer?
Yoriichi was born with the Mark of a Sun-Breather in a time before Breathing Styles even existed. He didn't speak until he was seven years old, leading his family to believe he was hard of hearing. His mother would pray to the Sun gods for him to be able to hear and gave him the Hanafuda Earrings as charms. He was a master swordsman even as a child thanks to his ability to see into the Transparent World.
Yoriichi could see inside people's bodies and watch his opponent's muscle contractions in order to predict how they were going to move. Much later in his life, after his wife and unborn child were killed by demons, Yoriichi met members of the Demon Slayer Corps and taught them Breathing Styles. though none of them could wield Sun-Breathing -- not even his own twin brother.
Yoriichi Tsugikuni Almost Defeated Muzan
When Yoriichi had a fateful encounter with Muzan Kibutsuji, he compared the Progenitor of Demons to a magma erupting from a volcano, boiling and seething as if to consume everything. He knew then and there that he was born with the power of Sun-Breathing for the sole purpose of defeating Muzan. In fact, Yoriichi defeated Muzan in an instant in such a perfect display of swordsmanship that Kibutsuji's cells still tremble hundreds of years later when reminded of the encounter. Unfortunately Yoriichi had a question for Kibutsuji before eliminating him, which allowed the latter to escape.
Yoriichi considered himself a failure for allowing Muzan to slip through his hands at the same time it became known that his own brother decided to become a demon known as Kokushibo, Upper-Rank One of the Twelve Kizuki. Yoriichi considered Sun-Breathing to be a sort of divine power he was blessed with, and it pained him that he failed to use his gift to rid the world of demons.
Are Yoriichi and Tanjiro Related in Any Way?
When Yoriichi was still a Demon Slayer, he saved the Kamado family from demons and remained a close friend of the family. After he had failed to defeat Muzan and watched his brother become a demon, he visited the Kamado family one last time. While he was there, Suyako (the mother) asked to see the forms of Sun-Breathing and Sumiyoshi (the father) burned them into his memory as Yoriichi performed them. When Yoriichi handed over his Hanafuda Earrings, the Kamado family knew they would never see him again, and they vowed to pass down Sun-Breathing to their descendants in honor of their debt to him.
It appears to be nothing more than a simple coincidence that the Kamado men have the same auburn hair as Yoriichi, and the Hanafuda Earrings they've passed down that Tanjiro now wears are the very pair once worn by Yoriichi himself. While the Kamados passed down the forms of Sun-Breathing with near-perfect accuracy, it wasn't until Tanjiro that they were put to use. The divine nature of Sun-Breathing is the reason Tanjiro looks like Yoriichi, even though the two are not related. Muichiro Tokito is the only living blood relative of Yoriichi. The Mist Hashira is the descendant of the child that Michikatsu Tsugikuni, Yoriichi's twin brother, left behind when he became a Demon Slayer and later a demon.
Yoriichi and Tanjiro are connected by way of being chosen to wield Sun-Breathing, but Yoriichi died long after his wife and child had died, meaning he had no direct descendants. In the Demon Slayer manga's final chapter, Yoriichi and his family have been reincarnated and are seen in the deep background of a panel as Tanjiro's own descendants head to school.