So I looked at the halopedia page for Halo Silentium and in the official summary it said this "Evidence-gathering agents known collectively as Catalog have been dispatched to collect testimony from the Librarian and both Didacts: the Ur-Didact, treacherously abandoned in a Flood-infested system, and the Bornstellar Didact, who accompanies the Librarian as she preserves specimens against the dire possibility of Halo extermination". It's saying that theirs 2 Didact which we already know, but it reveals that the ur-Didact was abandonded in a flood infested system, so it sounds like Faber just put him in there and thought that would basically be his execution, just leaving him with the flood.