Ukiyo is Majima's adopted sister and youngest sister of Ageha.
When Miyamoto Musashi 宮本武蔵 flees with Majima Gorohachi 真島五六八 after being deceived in the secret mission, Majima tells him he fears he doesn't have much time left. He asks that he bring his sword to his younger sister. After that, Majima falls, cutting a bridge across a deep chasm to prevent the soldiers chasing the two.
Musashi returns to the village to find Ukiyo and bring her her brother's sword, only to find that she was, in fact, not really Majima's sister. In an earlier scene, Majima alluded to some kind of murderous past for which he expressed regret. In that past, Majima had killed Ukiyo's father.
Ukiyo won't accept the sword. It's not so much that she hates Majima for what he did; it was really also her father's fault for dueling with the man. But, she won't accept it, no matter how hard Musashi tries. He stays with her there, trying to get her to accept the sword, but fails.
She doesn't seem to hate the way of the sword, however. She ties bells to Musashi's weapons, on the sword guards, and tells him to return to his swordsman life.
But Musashi refuses. He'd rather help her plant rice in her rural village. Unfortunately, men appear, seeking the bounty on Majima's head. They fight Musashi, who also has a bounty on his head, and in the struggle end up killing Ukiyo. Fatally wounded, Ukiyo tells Musashi that someone strong at swords, like him, has an onus to protect those who need him.
Of course, the old cliche' of someone racing to the scene and immediately assuming the man trying to help was the murderer arises. Musashi will always be blamed for Ukiyo's death, although he was trying to protect her from the inevitable people who would come looking for Majima. But, the key point here is that Musashi now has a reason to wield his swords."