In the bilge pump room I finally found the first hard evidence of sabotage; large cogs removed from the mechanism, with tools nearby which were obviously used to remove them. The hallucination of one of Mandus' children appearing and then exploding into a cloud of blood confirmed that they're already dead (whatever happened to them). Here's my working hypothesis so far, after six hours and having just finished the bilge pump room.
1. Mandus was a high achieving 19th century industrialist of the '
Better Living Through Steam' school of thought. He was already a bit of a nutter for progress through industrialism.
2. At some point he went to Mexico, where he found a massive ancient pyramid (images and models of which can be found throughout the game), and had an arcane and probably supernatural encounter through which was revealed to him the design of a great Machine, which he realized could fulfill his vision.
3. He returned to London and built the Machine. It appears that people (especially children), from the nearby workhouse (and probably from the church as well), were used as a source of raw material for the Machine, the function of which was to create a large, cheap, powerful, and servile labour force by taking people (mainly children), and transforming them into human-pig hybrids, with most of the features of a pig and severely (probably permanently), reduced mental capacity.
I'm still not sure why he thought this was a good idea, or what work they're supposed to do, especially since pig trotters have basically zero dexterity in contrast with human hands. When not working, they are kept in cells, where they sob mournfully, play simple games, attempt to read, or simply sleep. It is clear they are not enjoying themselves, and the game attempts to evoke our pity at this point.
4. The local church was co-opted to support and promote Mandus' vision through a radically modified Christianity. The original priest either couldn't handle this or found out too much, and was promptly fed into the Machine (or fed to the pigs).
5. The government's interest in Mandus' Machine grew past the stage of admiration to the point of suspicion, and he was investigated (probably more than once). The investigators were either convinced that all was well or were quietly Machined.
6. At some point Mandus' mental state became completely unhinged, possibly as a result of the death of his children (which obviously took place before the game begins). They may even have been Machined. In the process of absolutely doing his nut, he decided to shut down the Machine through various acts of sabotage. He then went to bed and promptly forgot all about it.
7. The result is a Machine which is no longer functioning, and a human-pig hybrid labour force which is clearly no longer where it is supposed to be, and clearly not doing what it is supposed to do.
8. This leaves the question of where the human-pig hybrids are, and what they are doing. My guess is 'Somewhere in the city outside the Machine', and 'All kinds of unpleasantness'.