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Recent discoveries of copious amounts of dust in quiescent galaxies (QGs) at high redshifts (z ≳ 1 − 2) challenge the conventional view that these objects have a negligible interstellar medium (ISM) in proportion to their stellar mass. We made use of theSIMBAhydrodynamic cosmological simulation to explore how dust and cold gas evolve in QGs and are linked to the quenching processes affecting them. We applied a novel method for tracking the changes in the ISM dust abundance across the evolutionary history of QGs identified at 0 < z ≲ 2 in both cluster and field environments. The QGs transition from a diversity of quenching pathways, both rapidly and slowly, and they exhibit a wide range of times that elapsed between the quenching event and cold gas removal (from ∼650 Myr to ∼8 Gyr). Contrary to some claims, we find that quenching modes attributed to the feedback from active galactic nuclei (AGNs) 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. Prolonged grain growth on gas-phase metals appears to be the key mechanism for dust re-formation, which is effective within ∼100 Myr after the quenching event and rapidly increases the dust-to-gas mass ratio in QGs above the standard values (δ_DGR ≳ 1/100). Consequently, despite heavily depleted cold gas reservoirs, roughly half of QGs maintain little evolution of their ISM dust with stellar age within the first 2 Gyr following the quenching. Overall, we predict that relatively dusty QGs (M_dust/M_⋆ ≳ 10⁻³ − 10⁻⁴) arise from both fast and slow quenchers, and they are prevalent in quenched systems of intermediate and low stellar masses (9 < log(M_⋆/M_⊙) < 10.5). This strong prediction poses an immediate quest for observational synergy between, for example, theJames WebbSpace Telescope (JWST) and the Atacama Large Millimetre Array (ALMA).