After leaving Kokushibo's estate, Muzan did not return to his own quarters. Instead, he sat down on the stone steps just outside. The only reason he stayed was out of genuine concern that Kokushibo might do something foolish.
In the original timeline during the final battle in the Infinity Castle, Kokushibo had been utterly horrified by his own "ugly" appearance. Upon recalling his sinful life, he had simply chosen to give up and surrender to death—a classic case of profound body dysmorphia.
Muzan certainly did not want Kokushibo to die, yet he had no idea what to do to prevent it. If the swordsman truly saw through his own inner turmoil because of this and chose suicide or betrayal... for Muzan, that would truly spell absolute disaster.
Chapter 38