All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Marriage without the consent (and presence) of the Wali (bride's guardian) is invalid because the consent of the guardian is a condition for the validity of the marriage contract according to the most valid opinion of the jurists, and this is also the view of the majority of the scholars in contrast to Abu Haneefah who is of the opinion that it is valid. Therefore, this marriage must be annulled unless a Muslim judge has ruled that it is valid.
If there are any children resulting from this invalid marriage, they should bear the name of that man (the husband) due to the mistaken assumption; meaning that the man married that woman believing that the marriage was valid. For more benefit, please refer to Fatwa 86773 and 256939.
If they both want to continue the marriage, they should renew it fulfilling the conditions of a valid marriage contract as underlined in Fatwa 83629.
If this man has become righteous and bears a good moral character, then we recommend that he be allowed to marry her.
There is no doubt that the girl was absolutely wrong when she fled from the home of her guardian and got married without his consent. If he had refused marrying her off without a sound reason, then Islam provides a solution for such a case - that she takes her matter to an Islamic judge or whoever acts on his behalf, so that he would repel the harm from her and marry her off, as the ruler is the guardian of whoever has no guardian as confirmed in the authentic Sunnah. But she should not have fled as this opens a great gate to corruption. Hence, she is obliged to repent and seek the forgiveness of her parents. For more benefit, please refer to Fatwa 86527.
Finally, it should be noted that it is wrong to say that this girl will not be forgiven as long as her parents do not forgive her. This is a matter belonging to the Unseen and a person cannot speak about it without evidence. Allaah may forgive her for her unfulfilled duty to Him, while she is still obliged to fulfill the duty to her parent, and if she does not seek their forgiveness until she dies or until they die, then Allaah may make them content with her on the Day of Judgment in any manner that He wills. For more benefit, please refer to Fataawa 88067 and 89494.
Allaah Knows best.