All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
It is not permissible for a woman to live with a marriageable man in the same house, as this is one of the major reasons of temptation and a way for the devil to lure them to commit adultery or fornication. The Prophet said: "No man should stay in seclusion with a marriageable woman except in the presence of her Mahram (i.e. a non-marriageable relative.” [Al-Bukhari and Muslim] It is also confirmed that the Prophet said: "Beware of entering upon marriageable women." If this is the case with occasional seclusion or entering to women, so what about living together while probably sharing the same amenities, like hall, kitchen and the like, as the man could be in seclusion with her and the like, and this is forbidden. The man and woman being of such an age does not mean that they could not be tempted by each other.
Therefore, one must look for permissible means to solve this problem, like getting a separate accommodation; this is something possible in that country where the government provides an accommodation for the residents according to the law. We have been informed to this effect from people who live in that country.
Among other permissible means is for this woman to marry this man if he is a Muslim.
To conclude there is no necessity for this woman to live with this man according to the situation mentioned.
Allaah Knows best.