For a Muslim woman to marry a non-Muslim man is something that is prohibited, and it is a major sin and immoral action. This union is not regarded as a marriage; rather it is regarded as fornication and adultery. This ruling has been explained previously in fatwa no. 100148.
What this woman must do is hasten to leave this non-Muslim man immediately, and she must repent to Allah, may He be exalted, and ask Him to forgive her for what she has committed of this grave evil. It is not permissible for her to remain with him for a moment longer, or allow him to be intimate with her at all.
What you have mentioned about her not living with her parents does not justify her remaining in this adulterous relationship. She has to put her trust in Allah, may He be exalted, for Allah, may He be exalted, says (interpretation of the meaning):
“And whosoever fears Allah and keeps his duty to Him, He will make a way for him to get out (from every difficulty).
3. And He will provide him from (sources) he never could imagine. And whosoever puts his trust in Allah, then He will suffice him. Verily, Allah will accomplish his purpose. Indeed Allah has set a measure for all things”
Her leaving this man does not require a shar‘i divorce, because this marriage is invalid in and of itself, therefore it does not require a divorce.
She has to tell this man frankly that she made a mistake by marrying him, and that Islam prohibits that. So either he should become Muslim and do a new marriage contract with her, because the previous marriage contract is invalid according to Islamic teaching; or if he wants to continue to follow his own religion, then he must leave her, and she must leave him. In that case it is essential, to settle their legal situation, for him to divorce her officially.
If he refuses to do that, then she should resort to legal procedures, and give any reasons so that she may be divorced officially. Even though this marriage does not carry any weight and is annulled in and of itself, it is essential for her to get the official divorce, as we said, so that her legal situation will be settled, and so that she will have no obstacle to entering into an Islamic marriage in the future.
It is not permissible for her to marry anyone else until she has had one menstrual cycle after leaving him, to establish that she is not pregnant. That menstrual cycle should be counted from when she first leaves him, not from when she gets the legal divorce papers.
This woman should go to the Islamic centre in her city and ask them for help, for they will have the best knowledge of how to solve this problem from a legal point of view.
And Allah knows best.