  Stellar evolution theory predicts the existence of He-core remnants of the
primary components of intermediate-mass close binaries that lost most of their
H/He envelopes due to the mass exchange. They are expected to be observed as
(1-7) solar mass hot He-rich stars located in the HRD between sdO/B and
WR-stars. Several thousands of such stars are expected to exist in the Galaxy,
but none of them have been identified so far. We aim to provide comprehensive
predictions of the numbers and fundamental properties of He-stars and their
companions in the Galaxy. This is a necessary first step to guide observations,
to enable a comparison between evolutionary models and observed populations,
and to determine the feedback of He-stars in the Galaxy. We expanded the
previously considered space of parameters describing progenitors of He-stars
and applied a population synthesis based on a grid of models computed by the
code MESA. The estimated number of Galactic binaries hosting (1-7) solar mass
He-stars is about 20000; it declines to about 3000 for mass exceeding two solar
ones. The decisive factor that defines the number of He-stars is runaway mass
loss after Roche lobe overflow by primary components, resulting in formation of
common envelopes and merger of components. He-stars are much less numerous than
expected, since a fraction of close binaries with primary masses below (5-7)
solar ones produce subdwarfs with masses below solar. Overwhelming majority of
He-stars reside in binaries with an early-type companions and can be identified
neither by the UV excess nor by emission features. The large periods of a
significant fraction of binaries hosting stripped stars (exceeding several
hundred days) also hamper their discovery. (Abridged).
