All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
This sister has committed a serious mistake and an evident sin. What she did involves many violations of the Islamic Shariah, among which are the following:
First: getting pregnant in an illegitimate way. Allah has made the legitimate marriage the only way and means for having children. Allah says (what means): {And Allah has made for you from yourselves mates and has made for you from your mates sons and grandchildren and has provided for you from the good things. Then in falsehood do they believe and in the favor of Allah they disbelieve?} [Quran 16:72]
Ma'qil ibn Yasaar narrated, “A man went to the Prophet
and said, ‘I have found a woman of rank and beauty, but she does not give birth to children. Should I marry her?’ He said, ‘No.’ He again went to him and the Prophet again forbade him (from marrying her). He went to him a third time, and he (the Prophet) said, ‘Marry women who are affectionate and fertile, for I will be proud of your great number before the other nations.’” [Abu Daawood]
Second: the process of artificial insemination requires revealing the private parts, and it is not permissible for a woman to reveal them to other than her husband except for a legitimate necessity. Al-‘Izz ibn Abd As-Salaam said in his book Qawaa'id Al-Ahkaam, “Concealing one’s ‘Awrah (parts of the body that must be covered according to the Shariah) is obligatory, and it is one of the best acts of sense of honor, the most beautiful custom, especially in case of non-Mahram (marriageable) women, but this is permissible for necessities and dire needs…”
Mu‘aawiyah ibn Haydah asked the Prophet
“When and when should we not cover our ‘Awrah?” Thereupon, the Prophet
said, “Cover your ‘Awrah, except from your wife or what your right hand possesses.” [Abu Daawood, At-Tirmithi and Ibn Maajah]
Al-Munaawi said in his commentary on this hadeeth, “A woman should cover her ‘Awrah even from what her right hand possesses, with the exception of her husband.”
Third: the loss of lineage. It is not permissible to trace this child to the owner of this sperm if it was possible to identify him and know who he is, because he is not her legitimate husband. However, the newborn is attributed to the husband only, as in the hadeeth in which the Prophet : said, “The child is for the (owner of the) bed (i.e. the husband).” [Al-Bukhaari and Muslim]
For more benefit, please refer to fatwa 124459.
The preceding is in addition to other violations of Shariah. What you mentioned about her waiting for years and no one proposed to her for marriage and that she has reached an age at which she cannot bear children if she gets married does not justify the abominable act that she has committed.
Finally, it should be noted that the guardians should look for suitable husbands for their daughters, as this is permissible, and the best Companions of the Prophet did so, such as ‘Umar
who offered his daughter Hafsah in marriage to suitors.
It is also permissible for a woman to propose herself to a man for marriage provided that she abides by the Islamic etiquette, which we have already highlighted in fatwa 82471.
Allah knows best.