Is it permissible for a woman to remove her hijab if there is no other work available, and does this contradict lawful earnings?

There is no doubt that adultery and a woman removing her head covering are forbidden. However, what is forbidden becomes permissible out of dire necessity, such as when a woman fears for her life and finds no other recourse. This permissibility is limited to the extent necessary to avert harm, without exceeding it, based on Allah’s statement: ﴿But whoever is forced by necessity, neither desiring it nor transgressing its limit, there is no sin upon him. Indeed, Allah is Forgiving and Merciful.﴾ (Al-Baqarah: 173). This is also supported by the story of one of the three men upon whom the rock fell, where he refrained from committing adultery with his cousin after he had power over her, despite his extreme need. However, the crucial matter lies in verifying the existence of such a necessity.