What is the ruling on women's participation in demonstrations if there is a fear of them being exposed to thugs, arrest, or gunfire?

If what the questioner mentioned about women being exposed to impermissible things is true, then it is not permissible for them to go out in demonstrations, in order to preserve their honor and prevent fitna (strife/temptation). The permissibility of a woman participating in demonstrations is conditioned upon the permissibility of the demonstrations themselves, and that they are free from anything that would prevent her participation, such as her mixing with men, and the permission of her husband or guardian. Among the impediments to this outing is the strong presumption that the woman will be exposed to what has been mentioned. This is derived from the conditions for women going out for Jihad. If Jihad is conditioned upon their safety, then anything less is more so. The jurists have mentioned restrictions on women going out for Jihad, among them being that it should be in a large army where their safety is ensured, and that elderly women go out for service, while the going out of young women is disliked for fear of fitna.