What is the ruling on a Muslim woman continuing to wear the hijab despite being exposed to arrest, humiliation, and the risk of rape in a country that prohibits it, given her fear of removing it due to feeling "naked" without it?

If you are able to emigrate from this country to another, then it is obligatory for you to do so, fleeing with your religion and preserving your faith and chastity. If you are unable to, and if wearing the hijab would lead to harm to yourself, or your limbs, or your honor, or your mind, then it is permissible for you to uncover what wards off that harm out of necessity, provided that you do not leave your house except out of necessity, and that the uncovering is limited to warding off the harm. However, if wearing the hijab does not lead to significant harm, then it is not permissible for you to remove it, and you must be patient, and you will have a great reward.