We study the thermal and viscous stability of accretion flows in low-mass b
lack hole binaries (LMBHBs). We consider a model in which an inner advectio
n-dominated accretion flow (ADAF) is surrounded by a geometrically thin acc
retion disk, the transition between the two zones occurring at a radius R-t
r. In all known LMBHBs, R-tr appears to be such that the outer disks could
suffer from global thermal-viscous instability. This instability is likely
to cause the transient behavior of these systems. However, in most cases, i
f R-tr were slightly larger than the estimated values, the systems would be
globally stable. This suggests that a population of faint persistent LMBHB
s with globally stable outer disks could be present in the Galaxy. Such LMB
HBs would be hard to detect because they would lack large-amplitude outburs
ts and because their ADAF zones would have very low radiative efficiencies,
making the systems very dim. We present model spectra of such systems cove
ring the optical and X-ray bands.