Muzan Kibutsuji is the main antagonist of the Demon Slayer series. He was the first ever original demon, thus making him the Demon King. Muzan stands as one of the most ruthless and unabashedly evil characters in the entire show. Killing others is mere sustenance to him and he feels no remorse for doing so.
As the King of Demons, he rules with an iron fist, showing no mercy to even his own people. His stone-hearted behavior can be seen when he scolds Akaza for not finishing off Tanjiro and company by inflicting harm on him.
However, in episode 8, Muzan is seen being kind, some would even say human, towards two individuals. These were his wife and daughter, his family, though not the real ones of course. They are seen just that once and never again after. This led to anime fans asking - what did Muzan do to his family?
Demon Slayer: What happened to the little girl and the lady?
As mentioned, a lady and a child made an appearance with Muzan in episode 8. They were his human wife and daughter. The two were never seen again after that episode. Nothing is known about what happened to them.
Muzan was immortal as the King Demon, but even he was aware of certain drawbacks that it entailed. One was the weakness to sunlight. The other was disguise. It would be tougher for him to blend into society if he was always by himself. If word of his demonhood got out, no amount of immortality or shapeshifting could protect him from being hunted.
Thus, he keeps a human wife and child to make it easier for him to fit into society without raising suspicion. Not only that, it helps increase his social standing. Nonetheless, this is just speculation as no concrete answer is available. Muzan's family makes very brief appearances and are swept away as easily as they are introduced.
Over his long lifetime, Muzan had a number of families. This includes the one he was born into before becoming a demon. Additionally, he took 5 wives, making each one's life miserable. Repeated abuse and torture drove them to take their lives. But that did not stop him from repeating it to other women later on.
As for his biological family, it is understood that they carried on throughout the years as the Ubuyashiki Clan. Particular members of the Ubuyashiki Clan have an uncanny resemblance to Muzan. The members of the bloodline had also been cursed with short lifespans. That was until the Demon Slayer Corps ended Muzan at the series' culmination.
Interestingly, the Ubuyashikis became one of Muzan's greatest enemies in Demon Slayer. Kagaya Ubuyashiki stood as the 97th head of the Demon Slayer Corps.
Needless to mention, Muzan Kibutsuji was the progenitor of all the other demons in Demon Slayer. About a millennium ago, during the Heian Era, Muzan became a demon as the result of an experimental treatment in an attempt to cure his terminal illness. Since then, his aim has been to live without fearing death and become truly eternal. Muzan devised two methods to achieve this:
Find the Blue Spider Lily or create more demons till one day one of them would conquer their weakness to sunlight.
Thus began his quest for the Blue Spider Lily and obsession for finding the one demon immune to the sunlight.