  Recently E-665 reported the first measurement of soft ($E_n \le 10 $MeV)
neutron production in deep inelastic scattering (DIS) off nuclei. We report the
first theoretical analysis of the data. We find that the observed cross section
can be quantitatively explained as due to the final state interactions (FSI) of
low energy nucleons ($E_N \sim 200-400 MeV$) produced in the elementary $\mu N$
interactions. We argue that the data indicate strong a suppression of the FSI's
of fast partons (hadrons) in DIS at high energies, and that studies of the soft
neutron production would provide a new sensitive probe of the dynamics of FSI's
in DIS both at fixed target energies and at the HERA $eA$ collider.
