  Arguments in favor of a light $\Xi NN$ hypernucleus with $(I)J^P=(3/2)1/2^+$
are presented, within the uncertainties of our knowledge of the baryon-baryon
strangeness $-2$ interactions. If bound, this $\Xi NN$ state, being decoupled
from the lowest $N\Lambda\Lambda$ system, would be stable. It will also benefit
from additional binding due to the electromagnetic interaction what makes it
worthwhile to look for. We show how the equivalent state with $J=3/2$ could
never be bound in spite of the attractive interaction of the two-body
subsystems. We illustrate our discussion with a full-fledged Faddeev
calculation of the $\Xi NN$ system using simple potentials that mimic more
elaborate interactions. We also make contact with different recent
phenomenological interactions from the literature, like the ESC08 Nijmegen
potential or quark-model based potentials.
