There's a missing link.

It's the way the semi-soluble Silver complexes link and bond to the cellulose in Fibre based paper (the base). This is why films and RC papers can tolerate higher silver levels in working fixer than FB papers and suffer no long term ill effects.

It's many years since I looked at all the equilibrium reactions taking place during fixing, and the complexes formed, I have a schematic diagram somewhere (I drew/typed it in 1976) not sure where at the moment. At that time few in the UK were using Sodium Slphite based wash aids, in fact some still used Peroxide or similar hypo eliminators, now long discredited.

Essentially the use of Sulphite helps reverse some equlibrium reactions from less soluble to more soluble complexes. It's not a miracle cure for very poorly fixed prints though.