Notice I say “mass disappearances”.
Killers, hunger, illness and hangings don’t make people disappear. They leave corpses. In Fallen London’s case those corpses quite often later reanimate and continues being part of the city. And in any case, enough of these events together will get noticed. If Jack starts killing people, it’s not exactly a mystery. A mob will form and lynch him. Hangings are very loud. Hunger will actually make people riot. A government that kidnaps enough of it’s own people to depopulate a part of the city? Okay, I can believe that. A government that does the same and nobody notices? Would be no easier to conceal, than an epidemic of Black Plague.
Special Constables are probably taking some people away for various reasons, but if it was enough to affect the city, I think we would know.