We address the possibility that intelligent civilizations that destroy themselves could present signatures observable by humanity. Placing limits on the number of self-destroyed civilizations in the Milky Way has strong implications for the final three terms in Drake's Equation, and would allow us to identify which classes of solution to Fermi's Paradox fit with the evidence (or lack thereof). Using the Earth as an example, we consider a variety of scenarios in which humans could extinguish their own technological civilization. Each scenario presents some form of observable signature that could be probed by astronomical campaigns to detect and characterize extrasolar planetary systems. Some observables are unlikely to be detected at interstellar distances, but some scenarios are likely to produce significant changes in atmospheric composition that could be detected serendipitously with next-generation telescopes. In some cases, the timing of the observation would prove crucial to detection, as the decay of signatures is rapid compared with humanity's communication lifetime. In others, the signatures persist on far longer timescales.