Mucopolysaccharidosis, type IIIB (MPS IIIB) is a rare disease caused by mutations in the N-alpha-acetylglucosaminidase (NAGLU) gene resulting in decreased or absent enzyme activity. On the cellular level, the disorder is characterized by the massive lysosomal storage of heparan sulfate (HS)—one species of glycosaminoglycans. HS is a sulfur-rich macromolecule, and its accumulation should affect the turnover of total sulfur in cells; according to the studies presented here, it, indeed, does. The lysosomal degradation of HS in cells produces monosaccharides and inorganic sulfate (SO42−). Sulfate is a product of L-cysteine metabolism, and any disruption of its levels affects the entire L-cysteine catabolism pathway, which was first reported in 2019. It is known that L-cysteine level is elevated in cells with the Naglu−/− gene mutation and in selected tissues of individuals with MPS IIIB. The level of glutathione and the Naglu−/− cells’ antioxidant potential are significantly reduced, as well as the activity of 3-mercaptopyruvate sulfurtransferase (MPST, EC 2.8.1.2) and the level of sulfane sulfur-containing compounds. The direct reason is not yet known. This paper attempts to identify some of cause-and-effect correlations that may lead to this condition and identifies research directions that should be explored.