  In the framework of a simple quantum field theory describing the decay of a
scalar state into two (pseudo)scalar ones we study the pole(s) motion(s) of its
propagator: besides the expected pole on the second Riemann sheet, we find --
for a large enough coupling constant -- a second, additional pole on the first
Riemann sheet below threshold, which corresponds to a stable state. We then
perform a numerical study for a hadronic system in which a scalar particle
couples to pions. We investigate under which conditions a stable state below
the two-pion threshold can emerge. In particular, we study the case in which
this stable state has a mass of 38 MeV, which corresponds to the recently
claimed novel scalar state E(38). Moreover, we also show that the resonance
$f_{0}(500)$ and the stable state E(38) could be two different manifestation of
the same `object'. Finally, we also estimate the order of magnitude of its
coupling to photons.
