What is the ruling on traveling for work with a foreign woman who is not accompanied by a mahram?

A woman should be advised that her travel without a mahram is not permissible Islamically. This is by the consensus of scholars, except in specific cases such as Hajj and Umrah, leaving the land of shirk, or fleeing captivity.

If she does not comply, the nature of the travel should be considered. If it entails something forbidden, such as looking (at non-mahrams), seclusion (with a non-mahram), or mixing (of sexes), then the travel is not permissible. However, if it is possible to travel independently without any forbidden Islamic matters, then it is permissible.