My understanding is that consuming one's soul condemns them to the Void directly. So consuming them is what gave Braccus the ability to call them from the Void.
I am not 100% positive, but judging from the dialogue and the various books throughout my playthroughs, as well as the specific characters that were resurrected by Braccus in my playthrough (b/c some of those whose souls I consumed were not loyal to the God King in life), I think what happens is actually opposite of what you expected (and admittedly, me too). It was quite some time before I realized that consuming a soul sentenced them to the Void, but that is a direct line from dialogue somewhere (now I really wish I could remember which dialogue, so sorry). There are some characters who are sworn to the God King in life, so it stands to reason they would rise again at Braccus's command, and we knew from our first encounter with Voidsworn that their oath persists beyond death.
On the contrary, take for example the soul jars found in Act I. Smashing the jars sets the soul free, not to the Void. Consuming the soul in the jar sentences them to the Void. Leaving them as-is in the jar keeps them eternally bound between the world of the living and the Void.
If I've messed something up here, *please* correct me. I'm basing this all on my understanding from dialogue and text in my own playthroughs.
