  The trajectory of the first excited Efimov state is investigated by using a
renormalized zero-range three-body model for a system with two bound and one
virtual two-body subsystems. The approach is applied to $n-n-^{18}$C, where the
$n-n$ virtual energy and the three-body ground state are kept fixed. It is
shown that such three-body excited state goes from a bound to a virtual state
when the $n-^{18}$C binding energy is increased. Results obtained for the
$n-^{19}$C elastic cross-section at low energies also show dominance of an
$S-$matrix pole corresponding to a bound or virtual Efimov state. It is also
presented a brief discussion of these findings in the context of ultracold atom
physics with tunable scattering lengths.
