This note is somewhat bitter. It's about the software event horizon, beyond which a piece of software sucks and there is nothing you can do about it. It's something I encountered a couple of years ago, so hopefully it's far enough away, and I've filed off all the serial numbers. It was in another team. And besides, the project is dead.
It has been claimed that the single worst mistake you can make you can make on a big software project is to rewrite it from scratch. On the other hand, I believe there are situations where the best thing you can do is to throw it all away and start again. Presumably, these two situations are distinct, and the sign of an experienced developer is one who can choose the best course?
No. Sometimes, the code base is just screwed. It's dead, and you don't know it yet. You can rewrite from scratch, and it'll fail. You can maintain the existing code, and it'll just bog down and become a programmer trap, a developer black hole. In retrospect, you'll say you should have done the other thing.
However, you're just in a no-win situation. What can you do? Well, often it's not actually that bad. It'll be painful, but you can start retrofitting test harnesses, decoupling components, and pull the code base back to something where sensible decisions can be made. However, if your code has plenty of race conditions, relies on 'strategic leaks' and generally has bodge upon bodge upon bodge, it may be a no-hoper. I suggest firing the management involved for letting it get into this situation. Then fire their management for letting them do that. For bonus points, trawl through the source control logs for the very worst bugs introduced, and put the developers involved on the 'do not rehire' list (obviously they won't still be with you - such a project requires high turnover).
In summary, the best thing to do is to steer clear of such projects. For some reason, no-one believes it can be that screwed up, so whatever you do people will be unimpressed. Run away from a zombie code base while there's still time!