Is it permissible to marry a girl Islamically and officially without the knowledge of her family, given that her family has disowned her due to her past misconduct, and while granting her all the rights of a wife?

A woman's marriage without her guardian's permission is not valid. If she does so, the marriage is null and void according to most scholars, based on the hadith: "There is no marriage without a guardian." If the closest guardian refuses to give permission for marriage without a valid reason, guardianship transfers to the next in line or to the Sharia judge. If the parents prevent their child from marrying due to corruption in the woman's religion or character, then obedience to them is obligatory. The advice is to repent from the relationship, leave the girl, and search for a woman of religion and good character who pleases the family.