Is it permissible for a woman to drive a car out of necessity to avoid harm in Western countries, or if her husband is ill and unable to drive?

The basic principle is that it is permissible for a woman to drive a car, just as it is permissible for her to ride other means of transport. She is allowed to drive a car if it does not expose her to traveling with it or being in seclusion with non-mahram (definition) men, especially if there is a need for it, such as her husband's illness or the absence of a mahram to drive for her. If she is exposed to harm by walking, then her driving a car would be more protective and more safeguarding for her.