Not enough there to fall apart? The Black Imperium covers all of Segmentum Obscurus, half of Solar, and a noteworty portion of Ultima. That's a vast empire, and plenty of space for sufficient civil strife to bring the whole thing falling apart. Sure, someone will inevitably claim to be the successor to Abbadon's throne, but that's not the same as keeping the entire realm together. Unless someone acts to replace Abbadon very quickly and succeeds, you're probably looking at a few centuries of internal strife that will end with at least a half dozen or so large Chaos polities. Inevitably some of them will say they're the true inheritors, much in the same way various Petty Imperiums will be ruled by dudes who claim to be the new God Emperor, but they won't have the same legitimacy unless one of them becomes the Champion of Chaos Undivided like Abbadon is, and even then they won't have the thousands of years of inertia or even necessarily an external threat to unify the various factions against. Someone might be able to eventually get things back together, but that'll take even longer.