Here is the situation:
Father is foreigner, Mother originally Taiwan national, ten years ago she gave up Taiwan nationality, assumed husband’s nationality. Several children were born while mother was still Taiwan national, outside Taiwan. They have the father’s nationality. Can these children claim Taiwan nationality, since they were born to what was then a Taiwanese parent?
I would need more information in order to answer this question, including full details on the nationalities of each person (including the husband, wife, and children), when and where born, current location, current visa status and/or passport held, work status, educational background, etc.
Taiwan doesn’t pay much attention to international precedent, and additionally there are different procedures for people from different countries . . . . . . which depend to some degree on those countries’ diplomatic or economic relationships with Taiwan . . . . . .