What is the ruling on paying a sum of money and marrying off a man from the kidnapper's family to the kidnapped woman in exchange for the shame they incurred?

The abduction of a woman is a grave transgression committed by the abductor, and he must repent of it. Society must establish deterrents to prevent such acts.

If both parties agree to the payment of money and the marriage of a man from the perpetrator's family [to the woman] in exchange for the shame she endured, and the marriage is concluded with all its conditions met, then there is no objection to it.

However, if the perpetrator's family refuses the request of the woman's family, they are not obligated to fulfill it, as accountability rests with the perpetrator himself.

If it is proven that the abductor committed zina (unlawful sexual intercourse) with the woman, he deserves the prescribed punishment for zina, and she is entitled to a mahr al-mithl (a dowry equivalent to that of women of her status). If it is not proven, the ruler may discipline him and fine him as he deems appropriate.