Before Islam, there were many ways in which people were enslaved, such as selling a free person into slavery, enslaving someone due to debt, enslaving through force or deception, and enslaving prisoners of war. The Prophet ﷺ abolished all of these methods except one, which he allowed to continue. That one permissible form is the enslavement of prisoners of war. If non-Muslims are captured as a result of Muslims achieving victory in battle, the leader of the Muslims (Imam al-Muslimin) may enslave those prisoners. When one reflects on this, it becomes clear that enslaving a prisoner of war is actually an act of mercy toward them, since it allows them to live a normal life among people, whereas otherwise they would either be killed or imprisoned indefinitely.
It is therefore clear that in Islam, no free person can be made a slave, nor does any person have the right to voluntarily submit themselves to slavery. A person can only become a slave as a prisoner of war, and even then only by the decision of the leader of the Muslims.
Therefore, in the situation described in the question, making this woman a slave is not permissible and is forbidden in Islamic law. There is absolutely no allowance for this in the Shariah.
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دلائل:
سنن ابن ماجه: (رقم الحدیث: 2442، ط: دار الجیل)
عَنْ أَبِي هُرَيْرَةَ ، قَالَ: قَالَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ:" ثَلَاثَةٌ أَنَا خَصْمُهُمْ يَوْمَ الْقِيَامَةِ وَمَنْ كُنْتُ خَصْمَهُ خَصَمْتُهُ يَوْمَ الْقِيَامَةِ: رَجُلٌ أَعْطَى بِي ثُمَّ غَدَرَ، وَرَجُلٌ بَاعَ حُرًّا فَأَكَلَ ثَمَنَهُ، وَرَجُلٌ اسْتَأْجَرَ أَجِيرًا فَاسْتَوْفَى مِنْهُ وَلَمْ يُوفِهِ أَجْرَهُ".
مختصر القدوری: (232/1، ط: دار الکتب العلمیة)
ولا يفدون بالأسارى عند أبي حنيفة وقال أبو يوسف ومحمد: يفادى بهم أسارى المسلمين ولا يجوز المن عليهم وإذا فتح الإمام بلدا عنوة فهو بالخيار: إن شاء قسمه بين الغانمين وإن شاء أقر أهله عليه ووضع عليهم الخراج وهو في الأسارى بالخيار: إن شاء قتلهم وإن شاء استرقهم وإن شاء تركهم أحرارا ذمة للمسلمين، ولا يجوز أن يردهم إلى دار الحرب
Allah the Almighty knows best.
Darul ifta Al-Ikhlas, Karachi.