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Stellar evolution theory predicts the existence of He-core remnants of theprimary components of intermediate-mass close binaries that lost most of theirH/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 andWR-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 comprehensivepredictions of the numbers and fundamental properties of He-stars and theircompanions 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 thepreviously considered space of parameters describing progenitors of He-starsand applied a population synthesis based on a grid of models computed by thecode MESA. The estimated number of Galactic binaries hosting (1-7) solar massHe-stars is about 20000; it declines to about 3000 for mass exceeding two solarones. The decisive factor that defines the number of He-stars is runaway massloss after Roche lobe overflow by primary components, resulting in formation ofcommon envelopes and merger of components. He-stars are much less numerous thanexpected, since a fraction of close binaries with primary masses below (5-7)solar ones produce subdwarfs with masses below solar. Overwhelming majority ofHe-stars reside in binaries with an early-type companions and can be identifiedneither by the UV excess nor by emission features. The large periods of asignificant fraction of binaries hosting stripped stars (exceeding severalhundred days) also hamper their discovery. (Abridged).

Elusive hot stripped helium stars in the Galaxy I. Evolutionary stellar models in the gap between subdwarfs and Wolf-Rayet stars