Okay so first of it's not an exacat remake of Inuyasha, it's just that the characters are really similar and in some ways the plot as well. She remains in that time until the end.
I think it was some kind of jug or a vase which broke, but she does meet the guy that's like Inuyasha who was trapped and she saves him. There's also a princess/priestess who looks exactly like her, like Kikyo. The brother of the guy who's like Inuyasha hates him and looks like Sesshomaru, white hair and all, plus he saves a girl who ends up travelling with him, kinda like Rin but in the drama she's much older. There's also a woman who's like Sango.