Sometimes I think the "debt" analogy is too clean. Brian Foote and his coauthor used many analogies in his "Big Ball of Mud" paper, including "Shanty Town", but I think the best analogy for the products I've seen with large amounts of technical debt is "Slum".
Products with large technical debt are money-makers, in spite of their problems (until the problems cost too much).
Slums have slum-lords, who profit from lack of maintenance, who are ignoring the pain of the inhabitants (developers and tester), and who are also ignoring the benefits of a clean environment... (of course, you can only take an analogy so far).
Still, it takes an empowered group of inhabitants to transform a slum into a desirable place to live and work. That requires management support.