  We model the Galactic population of detached binaries that harbor black holes
with (0.5-1.7) solar mass companions -- the remnants of case B mass-exchange
that rapidly cross Hertzsprung gap after the termination of the Roche-lobe
overflow or as He-shell burning stars. Several such binaries can be currently
present in the Galaxy. The range of black hole masses in them is about 4 to 10
solar ones, the orbital periods are tens to hundreds day. The unique BH-binary
LB-1 fits well into this extremely rare class of double stars.
