  Under the assumptions that molecular clouds are nearly spatially and
temporally isothermal and that the density peaks (``cores'') within them are
formed by turbulent fluctuations, we argue that cores cannot reach a
hydrostatic (or magneto-static) state as a consequence of their formation
process. In the non-magnetic case, stabilization requires a Bonnor-Ebert
truncation at a finite radius, which is not feasible for a single-temperature
flow, unless it amounts to a shock, which is clearly a dynamical feature.
Instead, in this case, cores must be dynamical entities that can either be
pushed into collapse, or else ``rebound'' towards the mean pressure and density
as the parent cloud. Nevertheless, rebounding cores are delayed in their
re-expansion by their own self-gravity. We give a crude estimate for the
re-expansion time as a function of the closeness of the final compression state
to the threshold of instability, finding typical values $\sim 1$ Myr, i.e., of
the order of a few free-fall times. Our results support the notion that not all
cores observed in molecular clouds need to be on route to forming stars, but
that instead a class of ``failed cores'' should exist, which must eventually
re-expand and disperse, and which can be identified with observed starless
cores. In the magnetic case, recent observational and theoretical work suggests
that all cores are critical or supercritical, and are thus qualitatively
equivalent to the non-magnetic case. Our results support the notion that the
entire star formation process is dynamical, with no intermediate hydrostatic
stages.
