  Stable charged heavy leptons and quarks can exist and hide in elusive atoms,
bound by Coulomb attraction and playing the role of dark matter. However, in
the expanding Universe it is not possible to recombine all the charged
particles into such atoms, and the positively charged particles, which escape
this recombination, bind with electrons in atoms of anomalous isotopes with
pregalactic abundance, exceeding substantially the terrestrial upper limits.
This abundance can not be reduced in the dense matter bodies, if negatively
charged particles have charge -1. Therefore composite dark matter can involve
only negatively charged particles with charge -2, while stable heavy particles
with charge -1 should be excluded. Realistic scenarios of composite dark
matter, avoiding this problem of anomalous isotope over-production, inevitably
predict the existence of primordial "atoms", in which primordial helium traps
all the free negatively charged heavy constituents with charge -2. Study of the
possibility for such primordial heavy $\alpha$ particle with compensated charge
to exist as well as the search for the stable charged constituents in cosmic
rays and accelerators provide crucial test for composite dark matter scenarios.
