Catalyzes the removal of elemental sulfur and selenium atoms from L-cysteine, L-cystine, L-selenocysteine, and L-selenocystine to produce L-alanine. [sulfur carrier]-H + L-cysteine = [sulfur carrier]-SH + L-alanine Belongs to the class-V pyridoxal-phosphate-dependent aminotransferase family. Csd subfamily.