  In this Letter we propose a formation channel for low-mass X-ray binaries
with black hole accretors and non-degenerate donors via grazing tidal
encounters with subgiants. We estimate that in a typically dense globular
cluster with the core density of $10^5$ stars pc$^{-3}$, the formation rates
are about one binary per Gyr per 50-100 retained black holes. The donors --
stripped subgiants -- will be strongly underluminous when compared to subgiant
or giant branch stars of the same colors. The products of tidal stripping are
underluminous by at least one magnitude for several hundred million years, when
compared to normal stars of the same color, and differ from underluminous red
stars that could be produced by non-catastrophic mass transfer in an ordinary
binary. The dynamically formed binaries become quiescent low-mass X-ray
binaries, with lifetimes of about a Gyr. The expected number of X-ray binaries
is one per 50-200 retained black holes, while the expected number of strongly
underluminous subsubgiant is about half this. The presence of strongly
underluminous stars in a globular cluster may be indicative of black holes
presence.
