I assume Swain must've made a deal of sorts with the Demon.
Demons are stated to be timeless, so it will certainly outlive Swain. I also don't think Swain could have somehow subjugated or conquered the demon (even though Swain does say he 'conquered' it). It's unlikely Swain physically or magically dominated the Demon. So I'll assume Swain either cut a deal with it or somehow outwitted it.
A demon of secrets obviously wants to feed on secrets, and a man in a position of power such as Swain obviously has the means and motive to obtain secrets of everyone around him. So maybe the Demon is empowering Swain in exchange for a steady stream of secrets? Swain gains the secrets from the soul fragments he rips out of enemies, and the quotes he speaks after doing so are fat, juicy secrets the demon is feeding on.
Alternatively, Swain may have somehow outwitted the demon, and tricked it into subjugation. This seems most likely, as Swain probably wouldn't want to be fully dependant on a Demon that only helps him because of a fickle deal. The question then is how he did it.
Just some loose speculations and theories, just wanted to leave my thoughts here.