  Detailed analysis of the distribution of nuclear matter in the halo nucleus
$^{11}$Be is performed within the microscopic approach based on the flexible
variational basis of the functions of the "polarized" orbitals model. It is
shown that the proposed approach reproduces, in agreement with the experiment,
the most distinguishing features of the mass distribution in this system.
Taking into account the results of specific calculations and the exceptionally
high reliability of the experimental data on the nuclear density distribution
in the "tail" of $^{11}$Be, we make a conclusion about the existence of new
structures with the sizes considerably exceeding the size of the nucleus (up to
tens of $fm$) and the density being thousands times less that the typical
nuclear one.
