  We present 2D high-resolution hydrodynamic simulations of the relativistic
outflows of long-duration gamma-ray burst progenitors. We analyze the
properties of the outflows at wide off-axis angles, produced by the expansion
of the hot cocoon that surrounds the jet inside the progenitor star. We find
that the cocoon emission at wide angles may have properties similar to those of
the subclass of short-duration gamma-ray bursts with persistent X-ray emission.
We compute the predicted duration distribution, redshift distribution, and
afterglow brightness and we find that they are all in agreement with the
observed properties of short GRBs with persistent emission. We suggest that a
SN component, the properties of the host galaxies, and late afterglow
observations can be used as a crucial test to verify this model.
