A method for recovering metal and sulfur from a feed stream, comprising: providing a first electrolytic cell comprising: a first anolyte compartment configured to hold an anolyte; a first anode positioned within the first anolyte compartment in communication with the anolyte; a first catholyte compartment configured to hold a catholyte, wherein the catholyte comprises an alkali ion-conductive liquid; a first cathode positioned within the first catholyte compartment in communication with the catholyte; a first separator positioned between the first anolyte compartment and the first catholyte compartment, the first separator in communication with the anolyte of the first compartment and the catholyte of the first compartment, the first separator configured to non-selectively transport cations; and a first power source in electrical communication with the first anode and the first cathode; introducing an anolyte into the first anolyte compartment of the first electrolytic cell, wherein the anolyte comprises at least one of an alkali metal sulfide and an alkali metal polysulfide, a polar organic solvent that dissolves at least one of the alkali metal sulfide, alkali metal polysulfide, and that dissolves elemental sulfur, the anolyte further comprising at least one of a heavy metal, a heavy metal compound, and a heavy metal ion; introducing a catholyte into the first catholyte compartment of the first electrolytic cell, wherein the catholyte comprises an alkali ion-conductive liquid; applying a voltage to the first electrolytic cell that is sufficient to reduce at least one heavy metal ion to heavy metal; oxidizing at least one sulfide ion in the anolyte of the first anolyte compartment of the first electrolytic cell to form elemental sulfur; moving cations to pass through the first separator positioned between, and in communication with the first anolyte compartment and the first catholyte compartment, the cations passing from the first anolyte compartment to the first catholyte compartment; and reducing said cations in the catholyte compartment to form a heavy metal and an alkali metal. providing a first electrolytic cell comprising: a first anolyte compartment configured to hold an anolyte; a first anode positioned within the first anolyte compartment in communication with the anolyte; a first catholyte compartment configured to hold a catholyte, wherein the catholyte comprises an alkali ion-conductive liquid; a first cathode positioned within the first catholyte compartment in communication with the catholyte; a first separator positioned between the first anolyte compartment and the first catholyte compartment, the first separator in communication with the anolyte of the first compartment and the catholyte of the first compartment, the first separator configured to non-selectively transport cations; and a first power source in electrical communication with the first anode and the first cathode; a first anolyte compartment configured to hold an anolyte; a first anode positioned within the first anolyte compartment in communication with the anolyte; a first catholyte compartment configured to hold a catholyte, wherein the catholyte comprises an alkali ion-conductive liquid; a first cathode positioned within the first catholyte compartment in communication with the catholyte; a first separator positioned between the first anolyte compartment and the first catholyte compartment, the first separator in communication with the anolyte of the first compartment and the catholyte of the first compartment, the first separator configured to non-selectively transport cations; and a first power source in electrical communication with the first anode and the first cathode; introducing an anolyte into the first anolyte compartment of the first electrolytic cell, wherein the anolyte comprises at least one of an alkali metal sulfide and an alkali metal polysulfide, a polar organic solvent that dissolves at least one of the alkali metal sulfide, alkali metal polysulfide, and that dissolves elemental sulfur, the anolyte further comprising at least one of a heavy metal, a heavy metal compound, and a heavy metal ion; introducing a catholyte into the first catholyte compartment of the first electrolytic cell, wherein the catholyte comprises an alkali ion-conductive liquid; applying a voltage to the first electrolytic cell that is sufficient to reduce at least one heavy metal ion to heavy metal; oxidizing at least one sulfide ion in the anolyte of the first anolyte compartment of the first electrolytic cell to form elemental sulfur; moving cations to pass through the first separator positioned between, and in communication with the first anolyte compartment and the first catholyte compartment, the cations passing from the first anolyte compartment to the first catholyte compartment; and reducing said cations in the catholyte compartment to form a heavy metal and an alkali metal.