  The asymptotic form of the wave functions describing a freely expanding
Lieb-Liniger gas is derived by using a Fermi-Bose transformation for
time-dependent states, and the stationary phase approximation. We find that
asymptotically the wave functions approach the Tonks-Girardeau (TG) structure
as they vanish when any two of the particle coordinates coincide. We point out
that the properties of these asymptotic states can significantly differ from
the properties of a TG gas in a ground state of an external potential. The
dependence of the asymptotic wave function on the initial state is discussed.
The analysis encompasses a large class of initial conditions, including the
ground states of a Lieb-Liniger gas in physically realistic external
potentials. It is also demonstrated that the interaction energy asymptotically
decays as a universal power law with time, $E_\mathrm{int}\propto t^{-3}$.
