Not yet reviewed by Pith; the record is open.

Recent discoveries of copious amounts of dust in quiescent galaxies (QGs) at high redshifts ($z\gtrsim 1-2$) challenge the conventional view that these objects have poor interstellar medium (ISM) in proportion to their stellar mass. We use the SIMBA cosmological simulation to explore the evolution of dust and cold gas content in QGs in relation to the quenching processes affecting them. We track the changes in the ISM dust abundance across the evolutionary history of QGs identified at $0 \lesssim z \lesssim2$ in the field and cluster environments. The QGs quench via diverse pathways, both rapid and slow, and exhibit a wide range of times elapsed between the quenching event and cold gas removal (from $\sim650$ Myr to $\sim8$ Gyr). We find that quenching modes attributed to the feedback from active galactic nuclei (AGN) do not affect dust and cold gas within the same timescales. Remarkably, QGs may replenish their dust content in the quenched phase primarily due to internal processes and marginally by external factors such as minor mergers. The key mechanism for re-formation of dust is prolonged grain growth on gas-phase metals, it is effective within $\sim100$ Myr after the quenching event, and rapidly increases the dust-to-gas mass ratio in QGs above the standard values ($\delta_{\rm DGR}\gtrsim1/100$). As a result, despite heavily depleted cold gas reservoirs, roughly half of QGs maintain little evolution in their ISM dust with stellar age within the first 2 Gyr following the quenching. Overall, we predict that relatively dusty QGs ($M_{\rm dust}/M_{\star}\gtrsim10^{-3}-10^{-4}$) arise from both fast and slow quenchers, and are prevalent in systems of intermediate and low stellar masses ($9<\log(M_{\star}/M_{\odot})<10.5$). This prediction poses an immediate quest for observational synergy between e.g., James Webb Space Telescope (JWST) and the Atacama Large Millimeter Array (ALMA).