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Observations of cold molecular gas reservoirs are critical for understandingthe shutdown of star formation in massive galaxies. While dust continuum is anefficient and affordable tracer, this method relies upon the assumption of a"normal" molecular-gas to dust mass ratio, $\delta_{\mathrm{GDR}}$, typicallyof order one hundred. Recent null detections of quiescent galaxies in deep dustcontinuum observations support a picture where the cold gas and dust has beenrapidly depleted or expelled. In this work, we present another viableexplanation: a significant fraction of galaxies with low star formation perunit stellar mass are predicted to have extreme $\delta_{\mathrm{GDR}}$ ratios.We show that simulated massive quiescent galaxies at $0 < z < 3$ in the\textsc{simba} cosmological simulations have $\delta_{\mathrm{GDR}}$ valuesthat extend $>$4 orders of magnitude. The dust in most simulated quiescentgalaxies is destroyed significantly more rapidly than the molecular gasdepletes, and cannot be replenished. The transition from star-forming toquiescent halts dust formation via star formation processes, with dustsubsequently destroyed by supernova shocks and thermal sputtering of dustgrains embedded in hot plasma. After this point, the dust growth rate in themodels is not sufficient to overcome the loss of $>$3 orders of magnitude indust mass to return to normal values of $\delta_{\mathrm{GDR}}$ despite havinghigh metallicity. Our results indicate that it is not straight forward to use asingle observational indicator to robustly pre-select exotic versus normalratios. These simulations make strong predictions that can be tested withmillimeter facilities.

High Molecular-Gas to Dust Mass Ratios Predicted in Most Quiescent Galaxies