  We investigate the connection between X-ray and radio-loud AGNs and the
physical properties of their evolved and massive host galaxies, focussing on
the mass-related quenching channel followed by $\mathcal{M}^\star (\simeq
10^{10.6} M_\odot)$ galaxies in the rest-frame NUVrK colour diagram at $0.2 < z
< 0.5$. While our results confirm that (1) radio-loud AGNs are predominantly
hosted by already-quenched and very massive ($M_*>10^{11}M_\odot$) galaxies,
ruling out their feedback as a primary driver of $\mathcal{M}^\star$ galaxy
quenching, we found that (2) X-ray AGNs affected by heavy obscuration of their
soft X-ray emission are mostly hosted by $\mathcal{M}^\star$ galaxies that are
in the process of quenching. This is consistent with a quenching scenario that
involves mergers of (gas-poor) $\mathcal{M}^\star$ galaxies $after$ the onset
of the quenching process, i.e., a scenario where $\mathcal{M}^\star$ galaxy
mergers are not the cause but rather an aftermath of the quenching
mechanism(s). In that respect, we discuss how our results may support a picture
where the slow quenching of $\mathcal{M}^\star$ galaxies happens due to
halo-halo mergers along cosmic filaments.
