  What happened to the central cores of tidally destructed dark matter clumps
in the Galactic halo? We calculate the probability of surviving of the remnants
of dark matter clumps in the Galaxy by modelling the tidal destruction of the
small-scale clumps. It is demonstrated that a substantial fraction of clump
remnants may survive through the tidal destruction during the lifetime of the
Galaxy if the radius of a core is rather small. The resulting mass spectrum of
survived clumps is extended down to the mass of the core of the cosmologically
produced clumps with a minimal mass. Since the annihilation signal is dominated
by the dense part of the core, destruction of the outer part of the clump
affects the annihilation rate relatively weakly and the survived dense remnants
of tidally destructed clumps provide a large contribution to the annihilation
signal in the Galaxy. The uncertainties in minimal clump mass resulting from
the uncertainties in neutralino models are discussed.
