  We use exact four-boson scattering equations in the momentum-space framework
to study the universal properties of shallow Efimov tetramers and their
dependence on the two-boson scattering length. We demonstrate that, in contrast
to previous predictions, the shallow tetramer in a particular experimentally
unexplored regime is not an unstable bound state but an inelastic virtual
state. This leads to a resonant behaviour of the atom-trimer scattering length
and thereby to a resonant enhancement of the trimer relaxation in ultracold
atom-trimer mixtures.
