Is this a maintenance job (just keep it running) or do they expect you to constantly add features/options ontop?
If they expect you to do significant 'patches' into it, you may simply have to write up your assessment of the system and make recomendations and leave it upto them to either carry out proper reworking of it (== $$$), or otherwise tell them you cant do what they need under their limitations.
Ive done maintenance/bug fixing as part of my job after the original programmers were long gone and was able to stabilize it and add error tracking and such (old C days when the bulk of that original code didnt even check function return codes and first thing was to add error checking logging/reporting everywhere it was like that, to actually determine what was failing to help debugging - that without changing the process logic much which took me 6 months to get a grip on to be able to do significant changes). Of course that was probably a smaller and not such a 'rat nested' mess as what you describe.
ADDED :
Just read that you gave notice. But to fill the time you can still write up your commentary and explain what they need to do to just start beating it into shape for its future (if it is important to their profit line and fragile enough that it WILL require changes to keep it running)
--------------------------------------------[size="1"]Ratings are Opinion, not Fact