Catalyzes the removal of elemental sulfur and selenium atoms from L-cysteine, L-cystine, L-selenocysteine, and L-selenocystine to produce L-alanine, and transiently retains the released sulfur atom on a cysteine residue, in the form of a persulfide. Can also desulfinate L-cysteine sulfinate (3-sulfino-L-alanine), which is the best substrate of the enzyme. Functions as a selenium delivery protein in the pathway for the biosynthesis of selenophosphate. Seems to participate in Fe/S biogenesis by recruiting the SufBCD-SufE proteins. Transfers sulfur to CsdE that increases the cysteine desulfurase activity of CsdA. Can also transfer sulfur directly to TcdA/CsdL in vitro. Appears to support the function of TcdA in the generation of cyclic threonylcarbamoyladenosine at position 37 (ct(6)A37) in tRNAs that read codons beginning with adenine. [sulfur carrier]-H + L-cysteine = [sulfur carrier]-SH + L-alanine AH2 + L-selenocysteine = A + H(+) + hydrogenselenide + L-alanine 3-sulfino-L-alanine + H2O = H(+) + L-alanine + sulfite Cysteine desulfurase activity is increased 2-fold in the presence of CsdE. Optimum pH is around 7.0 and 7.5 for the removal of selenium and sulfur atoms from L-selenocysteine and L-cysteine, respectively. Homodimer. Forms a heterodimer with CsdE. Induced in persister cells. Cells lacking this gene display a high decrease in the level of ct(6)A modification in tRNAs, and show the t(6)A modification instead. They also exhibit a fitness defect, are unable to swim, and are more resistant to the norfloxacin antibiotic than the wild-type. Belongs to the class-V pyridoxal-phosphate-dependent aminotransferase family. Csd subfamily.