What is the law in ISLAM regarding woman working outside the home, e.g. as an housemaid in an other country and without "mahram"? Is it permissible in ISLAM ?
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.
A woman is not allowed to travel without being accompanied by her Mahram. Similarly, it is not allowed for her to live in a house with a non-Mahram man whether the purpose of living is to serve, etc., except if she lives in a separate accommodation.
However, if she lives beside the accommodation of a non-Mahram man, then the facilities such as a passage, toilet etc., should be separate for her.
Ibn Hajar said: “If a woman lives in a room beside or upstairs or below the room of a non-Mahram man, the facilities such as kitchen, toilet, passageway, terrace etc., should not be common between them. Living in an accommodation sharing the above facilities is forbidden, because this will more likely cause mixing, and being in seclusion with each other, which are forbidden in the Sharee'ah. If they have separate facilities from each other but there is an open door between them, or the door of one of them opens into the other's room, or the passage is through the other's room, then living in such a place is also forbidden.”
Allah knows best.
You can search for fatwa through many choices