What should a Muslim woman do in this situation, if her 16-year-old cousin intends to run away from her family to avoid abuse and forced marriage after they return to their home country?

It is not permissible for your cousin to run away from her family and live with another family, as this constitutes disobedience to her parents, harms them and their reputation, and poses great dangers to her faith. Her family's mistreatment does not justify this, because the consequences of disobedience are dire in this world and the hereafter, as the Prophet, peace and blessings be upon him, said: "Two doors whose punishment is hastened in this world: oppression and disobedience."

She must return to her family, honor them, endure harm, and pray for their guidance. If her father insists on marrying her to an unsuitable person or rejects a qualified suitor, she should refer her case to the Sharia court. It is not permissible for her to marry herself without her guardian's permission, because her marriage is invalid, as the Prophet, peace and blessings be upon him, said: "There is no marriage except with a guardian" and "Any woman who marries without the permission of her guardian, her marriage is invalid."

You must advise your cousin with what has been mentioned. If she insists on running away, you must inform her family to prevent this evil. The father should also be advised and reminded of Allah and warned against oppressing his children.