We report the detection of cold dust in an apparently quiescent massive galaxy (log (M_∗/M_☉) ≈ 11) at z ∼ 2 (G4). The source is identified as a serendipitous 2 mm continuum source in a deep ALMA observation within the field of Q2343-BX610, a z = 2.21 massive star-forming disc galaxy. Available multiband photometry of G4 suggests redshift of z ∼ 2 and a low specific star formation rate (sSFR), log (SFR/M_∗)[yr⁻¹] ≈ −10.2, corresponding to ≈1.2 dex below the z = 2 main sequence (MS). G4 appears to be a peculiar dust-rich quiescent galaxy for its stellar mass (log (M_dust/M_∗) = −2.71 ± 0.26), with its estimated mass-weighted age (∼1–2 Gyr). We compile z ≳ 1 quiescent galaxies in the literature and discuss their age–∆MS and log (M_dust/M_∗)–age relations to investigate passive evolution and dust depletion scale. A long dust depletion time and its morphology suggest morphological quenching along with less efficient feedback that could have acted on G4. The estimated dust yield for G4 further supports this idea, requiring efficient survival of dust and/or grain growth, and rejuvenation (or additional accretion). Follow-up observations probing the stellar light and cold dust peak are necessary to understand the implication of these findings in the broader context of galaxy evolutionary studies and quenching in the early universe.