What is the ruling on a girl who ran away with an "irreligious" man and married him without her family's knowledge, then her father approved the completion of the marriage to cover his daughter after her return home?

It is not permissible for a girl to run away from her guardian's home merely because her father refuses her marriage to a specific man. If her father prevents her from marrying a suitable match, she has the right to refer the matter to the Sharia judge, or to the authorities responsible for Muslim affairs in non-Islamic countries if there is no Sharia judge. The guardian is a condition for the validity of the marriage. If the marriage takes place without a guardian, it is invalid and must be annulled. If the couple wishes to continue, they must renew the contract in the correct manner. Care and precision must be exercised in ascertaining the religion and character of the suitor.