A Dusty Quenching-Candidate AGN host at $z = 5.7$: massive quiescent galaxies may quench already during the dust-obscured phase

We present a spectro-photometric analysis of RUBIES-EGS-9809, a broad-line AGN-host galaxy at z=5.7 with a Balmer break and a dominant point-source component. The source is clearly dust reddened (AV≳3 mag), shows hot- and cold-dust emission, and is a Compton-thick X-ray emitter, with X-ray-to-bolometric ratio consistent with luminous AGN. The large AV agrees with a clear Na I absorption (EW=17±2 Å), possibly from a neutral-gas outflow (3-σ), while broad [O III] traces an ionized outflow, suggesting AGN feedback may be affecting the host. We estimate a stellar mass log(M⋆/M⊙)=10.7 ±0.3, Lbol∼4 × 10⁴⁶ erg s⁻¹, and a virial black-hole mass log(M•/M⊙)∼8.1 (subject to large systematics). The Balmer break is spatially resolved (0.1 arcsec, 0.6 kpc), consistent with a stellar origin, implying the galaxy is already old in stars while still heavily obscured. This shows that massive galaxies can host evolved stellar populations during their compact, dust-obscured phase, consistent with formation in an earlier dusty starburst. SED modelling suggests a declining SFR, but low-resolution spectroscopy alone cannot constrain the recent SFR, so we treat the source as a strong quenching candidate rather than a secure post-starburst system. Because quenching follows the decline in SFR, star-formation-driven outflows are disfavoured, leaving AGN feedback as a plausible driver. We speculate that such rapid feedback (∼100 Myr timescale) may precipitate quenching while the post-quenching phase stays dust-enshrouded, concealing the UV-bright quenched phase that would otherwise be easily detected, if dust free. By the time dust clears, the UV-luminous stars may have already dwindled, leaving a classic dust-free quiescent galaxy. This ‘dusty path’ to quiescence may explain the lack of intermediate-age quenched progenitors (ages 50–100 Myr) linking dusty starbursts to massive quiescent systems at z=3–7.