As the world’s population grows and resource consumption rises, there will be an increase in household waste and, consequently, the fly ash and slag from after the incineration of this waste need to be properly recycled or used as secondary raw materials in other industries. The authors of this work propose an innovative technology that has not yet been studied much in the literature; the obtained slag and fly ash are processed by plasma technology, and from those, fiber is formed. As shown by SEM studies, the raw material (before plasma–chemical treatment) consists of irregularly shaped granules or rod-shaped microforms. EDS studies show that both the original material and the products obtained after plasma–chemical processing are composed of various metal elements, but they make up a significantly small part, as the predominant elements are C, O, Cl, Si, and Ca. BET studies show that when the fiber is obtained with a plasma torch power of 55.5; 55.6 and 74 kW, respectively, the specific surface area is 11.9; 8.5 and 3 m2/g. It is worth noting that the raw material obtained after plasma–chemical processing is sufficiently clean and harmless to the environment, so it can be used as a secondary raw material, e.g., for the production of thermal insulation, in the production of catalysts, as a component in the production of concrete, or in other industries.