Catalyzes the removal of elemental sulfur atoms from cysteine to produce alanine. Seems to participate in the biosynthesis of the nitrogenase metalloclusters by providing the inorganic sulfur required for the Fe-S core formation. [sulfur carrier]-H + L-cysteine = [sulfur carrier]-SH + L-alanine Homodimer. Belongs to the class-V pyridoxal-phosphate-dependent aminotransferase family. NifS/IscS subfamily.