Byakuya of the Dream (夢幻の白夜) is Naraku's ninth and final detachment, meant to replace Kagura. His main purpose is to observe InuYasha and Moryomaru's growing powers and report back to Naraku.
After taking the power of one slash of InuYasha's Meidou Zangetsuha, he thinks to himself that the end is near, informing us that he knew he was going to die like the other incarnations. When Shippo sees him take the Meidou Zangetsuha's demonic energy, he is aware, but he doesn't capture Shippo, infact, he informs him that he has a chance to get out of Naraku's body alive. Later, Byakuya slashes Kagome with the blade that contained Meidou Zangetsuha's demonic energy. However, before he gets a chance at a second strike, InuYasha attacks him with his Meidou Zangetsuha and Byakuya is absorbed into it, but not before he states that he has fulfilled his purpose, and that he has no regrets. When Naraku dies, a Meidou appears behind Kagome, due to Byakuya's Meidou Blade.
He appears in manga chapter 433 and episode 4 in final act.
Powers & Abilities:
He has an incredible power to create illusions, but has many other powers as well: he can possess people with paper soldiers, summon vines to entrap his enemies, teleport others to different dimensions, detach organs from his body and erect barriers; making him essentially the most powerful of Naraku's detachments. He travels on a giant origami paper crane. He also has an ability to detach one of his eyes, which becomes a flying eye demon, which he uses to spy on his enemies. Naraku can also see what Byakuya sees by touching his eye socket, to which Byakuya finds "disgusting". Byakuya also has a fake sword (it is but a handle). This allows Byakuya's final techinque, in which the handle absorbs the demonic energy (which he used to make his own version of Inuyasha's Meidou Zangetsuha) and slashed Kagome. The purpose of this attack is still unknown as the Meido opened up behind Kagome some time after Naraku was defeated.
It is possible that he is a moth demon as he has many of the same powers such creating illusions he also seems to bear a resemblance to previous moth demons.
All information was obtained and quoted from the Inuyasha wikipage: "Byakuya-InuYasha." InuYasha Wiki. N.p., n.d. Web. <http://inuyasha.wikia.com/wiki/Byakuya>.