Recent discoveries of dust and molecular gas in quiescent galaxies (QGs) up to z ∼ 4 challenge the long-standing view that the interstellar medium depletes rapidly once star formation ceases, raising key questions of whether dust and gas coevolve in QGs, and how their depletion links to stellar aging. We present deep Atacama Large Millimeter/submillimeter Array Band 6 continuum and CO(3─2) observations of 17 QGs at z ∼ 0.4 in the COSMOS field. Using the dust-to-molecular gas mass ratio (δDGR) as a key diagnostic, we trace postquenching evolution of the cold interstellar medium. Our study triples the number of QGs with direct δDGR estimates, constraining 12 systems with stellar population ages of ∼5─10 Gyr. For the first time, we show that δDGR in QGs ranges from ∼8× below to ∼2.5× above the canonical value of δDGR ∼ 1/100. Despite uniformly low molecular gas fractions (median fH2=MH2/M⋆∼4.1% ), QGs follow diverse evolutionary paths: about half exhibit rapid (∼700 Myr) exponential dust decline with age, while the rest show mild decline over ≳2 Gyr, maintaining elevated δDGR ≳ 1/100. Our results support simulations' predictions of dust and molecular gas evolving independently postquenching, without a preferred quenching mode. This challenges the use of dust continuum as a H2 tracer, implying that quenching cannot be robustly linked to interstellar medium conditions when relying solely on dust or gas.