  The recently extracted matter radius of carbon isotope $^{22}$C allows us to
estimate the mean-square distance of a halo neutron with respect to the
center-of-mass of this nucleus. By considering this information, we suggest an
energy region for an experimental investigation of the unbound $^{21}$C virtual
state. Our analysis, in a renormalized zero-ranged three-body model, also
indicates that the two-neutron separation energy in $^{22}$C is expected to be
found below $\sim$0.4~MeV, where the $^{22}$C is approximated by a Borromean
configuration with a pointlike $^{20}$C and two $s$-wave halo neutrons. A
virtual-state energy of $^{21}$C close to zero, would make the $^{22}$C, within
Borromean nuclei configurations, the most promising candidate to present an
excited bound Efimov state or a continuum three-body resonance.
