We use a combination of high-resolution gas dynamics simulations of high-redshift dwarf galaxies and dissipationless simulations of a Milky Way-sized halo to estimate the expected abundance and spatial distribution of the dwarf satellite galaxies that formed most of their stars around z∼8, evolving only little since then. Such galaxies can be considered ``fossils'' of the reionization era, and studying their properties could provide a direct window into the early, pre-reionization stages of galaxy formation. We show that ∼5%-15% of the objects existing at z∼8 do indeed survive until the present in a Milky Way-like environment without significant evolution. This implies that it is plausible that the fossil dwarf galaxies do exist in the Local Group. Because such galaxies form their stellar systems early during the period of active merging and accretion, they should have a spheroidal morphology regardless of their current distance from the host galaxy. Their observed counterparts should therefore be identified among the dwarf spheroidal galaxies. We show that both the expected luminosity function and the spatial distribution of dark matter halos that are likely to host fossil galaxies agree reasonably well with the observed distributions of the luminous (LV≳106 L☉) Local Group fossil candidates near the host galaxy (d≲200 kpc). However, the predicted abundance is substantially larger (by a factor of 2-3) for fainter galaxies (LV<106 L☉) at larger distances (d≳300 kpc). We discuss several possible explanations for this discrepancy.