  It is commonly believed that accretion discs are truncated and their inner
regions are described by advection dominated accretion flows (ADAFs) in the
hard spectral state of black hole X-ray binaries. However, the increasing
occurrence of a relativistically blurred Fe K$\alpha$ line together with a hard
continuum points to the existence of a thin disc located near the innermost
stable circular orbit (ISCO). Assuming the accretion in the hard state is via
an ADAF extending to near 100 Schwarzschild radii, which is supplied by either
a stellar wind from a companion star or resulting from an evaporated disc, we
study the possible condensation of the hot gas during its accretion towards the
black hole. It is found that a small fraction of the ADAF condenses into a cold
disc as a consequence of efficient radiative cooling at small distances,
forming a disc-corona configuration near the ISCO. This takes place for low
accretion rates corresponding to luminosities ranging from $\sim 10^{-3}$ to a
few per cent of the Eddington luminosity. The coexistence of the weak inner
disc and the dominant hot accretion flow provides a natural explanation of the
broad K$\alpha$ line in the hard state. Detailed computations demonstrate that
such accretion flows produce a hard X-ray spectrum accompanied by a weak disc
component with a negative correlation between the 2-10 keV photon index and the
Eddington ratio. The predicted spectrum of Cygnus X-1 and the correlation
between the photon index and the Eddington ratio are in good agreement with
observations.
