Is there any liability on the questioner after he hit a woman with his car and fled, and she has not been found or her fate known?

If the woman caused the accident by crossing the highway, which is forbidden for pedestrians, and you were unable to avoid her and were adhering to traffic laws, then you are not liable. However, if you could have avoided the accident but failed to do so, then you are liable, and this includes blood money (Diyah) and expiation (Kaffarah). If it is not possible to obtain information about the injured woman after her death, the blood money should be paid to the Muslim treasury (Bayt al-Mal) or spent on their public interests.