About five years ago I started a fanfic starring Rin from Inuyasha, and in it she had been injured and then nursed back to health in a remote demon village. In order to save her, one of the demons fed Rin her blood, turning Rin into a half-demon (which I totally made up, of course – the only half-demons we ever see in the show are biological offspring of a human and a demon).
Don’t worry, this wasn’t just a plot device to get Rin and Sesshomaru together – they met much later when Rin had already been married and had a child. Nowadays I don’t support any version of a Rin-Sesshomaru romance, because no matter how old Rin would be, Sesshomaru would always be a father figure, and any romance between the two would be just wrong. Also, from what I’ve read of the manga, it seems that Kagura had feelings for Sesshomaru – that pairing would be sweet.