Naraku has been dead for two years now and Kagome has finally gone back to her own time where the well has finally sealed. Inuyasha who has been alone since that time has pretty much lived on his own all except visiting Sango, Miroku, and their children in the local village from time to time. During one of his visits he finally meets someone that "peaks" his interest. She is new to the village, someone he has never met before. Still, he does not trust her or want to get close to her, seeing as he had been hurt by Kikyo's death and Kagome's leaving.
Sango who "bumps" into the poor and ragged girl one day takes her under her wing as a younger sister and helps her out by taking her in, in exchange for recieving help with her and Miroku's 3 children. Natsuye agrees, seeing as she needs a place to live and that Sango is yet again pregnant with another child. Figuring they would both be able to help one another at least until she could get on her own two feet, Natsuye is left alone at the hut one day while everyone else is gone and Inuyasha shows up. Never having met a demon before she is of course scared where Inuyasha is his annoyed and usual unpleasant self. Natsuye who doesn't take likely to his snootieness tells him off even though she is petrified of him. I figure that is where their "relationsip" begins.