Catalyzes the removal of elemental sulfur from cysteine to produce alanine (PubMed:15220327). It supplies the inorganic sulfur for iron-sulfur (Fe-S) clusters (PubMed:10406803, PubMed:10551871, PubMed:15220327, PubMed:31040179). Plays a role in both tRNA-processing and mitochondrial metabolism (PubMed:15220327). Involved in the 2-thio-modification of both 5-carboxymethylaminomethyl-2-thiouridine in mitochondrial tRNAs and 5-methoxycarbonylmethyl-2-thiouridine (mcm5s2U) in cytoplasmic tRNAs (PubMed:14722066, PubMed:15220327, PubMed:8444805). [sulfur carrier]-H + L-cysteine = [sulfur carrier]-SH + L-alanine Optimum pH is 8.5. the N-terminal beta-strand formed by residues 99-104 is essential for the function. Impairs cysteine desulfurase activity of mitochondria. Leads to strong accumulation of free iron, not bound to heme or Fe/S clusters, in mitochondria, as well as to decreased amounts of the mitochondrial Fe/S proteins including aconitase and succinate dehydrogenase. Leads also to accumulation of 5-methoxycarbonylmethyluridine (mcm5U) and a concomitant decrease in 5-methoxycarbonylmethyl-2-thiouridine (mcm5s2U) in cytoplasmic tRNAs. Increases association between GRX5 and SSQ1 (PubMed:23615440). Present with 504 molecules/cell in log phase SD medium. Belongs to the class-V pyridoxal-phosphate-dependent aminotransferase family. NifS/IscS subfamily.