The dissolution of the Nephite nation did not remove the Gadiantons from the land, nor those who had supported them. Their attempted takeover of the government simply caused so much division that the Nephite government, as an overarching layer over the various cities and lands (and tribes), was dissolved.
Those who had been favorable to the Gadiantons, remained so, and gathered together in their own government. Over that reduced population, the Gadiantons declared a king. They had wanted a change to the government, and they made that change. They simply were not recognized by as many people.