A very interesting question, and althought I don't think I can answer it to full extend, I'll try to give some hints and we hope, that maybe somebody with more specific knowledge will arrive.

So first of all, there has to be drawn a line between extant and known texts. The great majority of the Roman fiction is lost to us and the glimpses we can get through attestations in other authors are to small to really get an insight.

However, when looking at a history of Roman literature, you will Not find anything, that comes close to "Self-Destruction Fiction". The reason for this is to be found in the way literature was produced that time. The modern writing typically favors novels. The Encyclopaedia Britannica defines novels in the following way: "Novel, an invented prose narrative of considerable length and a certain complexity that deals imaginatively with human experience, usually through a connected sequence of events involving a group of persons in a specific setting." The crucial point is "invented". While we take our pleasure in the invention of a fascinating hypothetical story, nearly all of classical writing Was restricted to mythological or historical motives. The Ancient societies apparently took their pleasure from the way the known subject was laid out before them. The only exception are the "classical novels" with only one extant book in Latin: Apuleius, Metamorphoses (we shouldn't count Petronius Satyricon). Here, the plot is completely fictional. But even those follow strict rules and have certain pieces of story to use. And, worst of all, they are made for a lower class audience, what gives them a plot like a typical washed up love story today. So the restrictions of writing about future events made it hard for them to express such thought in writing.

Still, I want to raise you one work that comes close to modern self-destructionary fiction. Lucanius' bellum civile. It deals with the war between Caesar and Pompey. This epos was a direct reaction to Virgil expressing the idea of a Rome in everlasting ascend culminating into the reign of Augustus. Lucan turned it completely around. Instead of an ascend to the harmony under Augustus, he saw the Roman history as a descend to the hells of Civil war. The slaughtering of anonymous masses and brother killing brother laid the stratum for the frenzy of the later emperors (at least in the latter part of the story). I guess this is closest we get to "Self-destruction Novels" we get. Still, there is one important lesson to be learned from Lucanus: The classic writing was restricted, but they were eager to give glimpses of their perception of present or even future through recounting past.

And here is, where we can find lots of examples of writers about Self-destruction. The historians were eager to declare the decadency of modern Rome and analyse the reason for a yet-to-come downfall (Sallustius, Tacitus), poems expressed (especially in Augustean Times) the joy of having passed the period of death and slaughter (Horatius, Virgilius) and Orators commented on the downfall of cities having in mind the thin ice the empire rests upon (Aelius Aristides, Dio Chrysostomos).

So, while there was no such literary subject as Self-destruction, still there was plenty of room for writers to express it.

I guess the best source for a overview of the subjects touched on above is a good history of latin literature. I usually use (althought german):

Michael von Albrecht, Geschichte der Römischen Literatur, Berlin / New York 1994.

Ahl, Frederick M. Lucan: An Introduction. Cornell Studies in Classical Philology 39. Ithaca, N.Y.: Cornell Univ. Pr., 1976. (This will prove useful, too)