  We report results of Chandra X-ray and VLA radio observations of the Galactic
accreting black hole V404 Cyg (GS 2023+338) in its quiescent state. V404 Cyg is
detected at its faintest level of radio and X-ray emission with a 0.5-10 keV
unabsorbed luminosity of 8.3 x 10^32 (d/3.5 kpc)^2 erg/s. The X-ray spectrum
fit with an absorbed power-law model yields a photon index of 2.17 +/- 0.13.
Contrary to previous findings, this clearly indicates that V404 Cyg undergoes -
like most black holes in quiescence - a softening of its X-ray spectrum at very
low luminosity compared to the standard hard state. The quiescent radio
emission is consistent with the presence of self-absorbed compact jets. We have
also reanalyzed archival data from the decay of the 1989 outburst of V404 Cyg
in order to quantify more precisely the correlation between radio and X-ray
emission in the hard state of V404 Cyg. We show that this correlation extends
over five decades in X-ray flux and holds down to the quiescent state of V404
Cyg. The index of this correlation (~0.5) may suggest that synchrotron
self-Compton emission is the dominant physical process at high energy in V404
Cyg. However, this index is also consistent with scale invariant jet models
coupled to an inefficiently radiating accretion disc. We discuss the properties
of the quiescent state of black holes and highlight the fact that some of their
properties are different from the standard hard state.
