Yakov Bok
The "Fixer" from the title, a Jewish carpenter living in Tsarist Ukraine. He doesn't have documentation, so he gets by doing odd jobs, until one day he is arrested for the murder of a Christian kid during the Passover holiday. His accusers try to beat a confession out of him, but he consistently denies any involvement.
Magistrate Bibikov
Yakov's best chance at being freed is the magistrate, Bibikov, but even Bibikov is not safe from the Tsarists, and he finds himself in solitary confinement just for associating with Yakov. He commits suicide.
Yakov's wife
Yakov's only consistent visitor is his wife who left him. She keeps him company, but only by bringing bad news and criticizing Yakov. Turns out, their child together is actually not even his. She'd had an affair and their child is someone else's.
Tsar Nicholas II
Yakov's story ends with an imaginary confrontation with the Tsar. Nicholas II has headed one of the most abominable governments in Russia's history, in Yakov's experience.