It seems that TV Tropes is no longer trying to hack my machine, which means it is time to get back to the action.
Someone who “suffers” from Chronic Backstabbing Disorder is a perpetual traitor, a person without any loyalties except one. Often it is loyalty to self but may also have a twisted sense of loyalty to a family member or loved one. This trope is one tool in the consummate survivor toolbox. Switching sides and selling out former comrades may well be their number one survival strategy even though in the long run their reputation for treachery almost always catches up to them. Which means keeping such a character around long enough for the chronic part of the story to kick in requires that said character is very good at covering their trail (by disposing of betrayed parties or foisting said betrayals on someone else) or always has something good enough to offer (real or imagined) the party they are seeking to ally themselves at the moment.
This trope is common in political dramas or historical plots such as long running civil wars where allegiances shift with the fortunes of the parties involved.