You still have not offered any details as to the relationship. What happens in other countries cannot be applied to Japan, especially if you are from a western country.
Anyway, it is a common practice in Japan and is more common than maybe you realize. How the Japanese themselves handle it these days I cannot say, (and neither can my Japanese wife), but I do know, from personal experience in Japan as a foreigner, that the woman, if she is working and chooses to live with you will, more than likely, offer to pay half out of respect. At least that's what I experienced on two occasions during my stay.
Maybe things have changed today, but after speaking to my Japanese wife, she says that if the woman is working and chooses to live with you, she should pay half, and offer to do so, unless you indicate otherwise. If not, she is probably "using you", probably as a "boy toy and accessory" and "a way to cut her own expenses" if you are just friends. (My wife's words, not mine).
As a poor, working student, when I was in Japan, I appreciated that the two women I lived with, who were working, offered, of their own volition, to pay half the expenses as it helped a lot. Not that it mattered much, mind you, but it was the reduced expenses on my part that helped and enabled me to save some money.
Your case may be wholly different, but without more details, it is quite difficult to offer advice other than personal experience.