Is it permissible for a woman to shake hands with a male teacher, who is a stranger to her, to avoid being fired from her job, and would her salary then be unlawful?

It is not permissible for a man to touch the body of a woman who is not lawful for him, nor for her to touch any part of his body, due to the Prophet's (peace be upon him) saying: "The hand commits zina (fornication/adultery), and its zina is touching." Therefore, he must repent sincerely. Fear of losing one's job does not justify committing forbidden acts. Whoever fears Allah, He will make a way out for him and replace it with something better. What happened is not considered flattery if it was not with the heart's consent. What he did does not affect his earnings if the original work was permissible and he performed it as required. It should be noted that working in mixed-gender environments is forbidden except out of necessity, and residing in lands of disbelief is forbidden except for a need or necessity.