Is a marriage that took place without the knowledge of the family or witnesses, and without mention of a dowry or written conditions, then was rejected by the husband's family, valid or void, and what should the wife do in this situation?

The described situation is not a marriage (nikah) but rather an illicit sexual relationship (sifah); because marriage has conditions and pillars without which it is not valid, including: the صيغة (ijab and qabul - offer and acceptance), the guardian (wali), and witnesses. Marriage is one of the great rituals of the religion; Allah called it a "solemn covenant." They must separate. If they engaged in it while knowing it was forbidden, then repentance is obligatory upon them. If they desire to marry, the marriage must fulfill the conditions of validity. If the young man cannot convince his parents to agree, he must leave her and look for another, for obedience to parents is obligatory unless he fears harm upon himself. It is not a condition for the validity of marriage that it include stipulations, and not naming the dowry does not invalidate the marriage; in this case, the woman is entitled to a dowry equivalent to that of women of her status (mahr al-mithl).