What is the ruling on fighting one who slanders a Muslim, accusing them ofzina, and is it permissible to kill them if they do not desist and continue slandering, in a country where there is no ruler who governs by the command of Allah?

It is not permissible to kill a Muslim except for one of three reasons: intentional killing, adultery after marriage, or apostasy and abandoning the community. Public shaming is not one of the justifications for shedding a Muslim's blood. The punishment for slander is eighty lashes, and the execution of punishments and Hadd (prescribed) penalties is not entrusted to individuals.