  Within the context of a hybrid strong/weak coupling model of jet quenching,
we study the consequences of the fact that the plasma produced in a heavy ion
collision cannot resolve the substructure of a collimated parton shower
propagating through it with arbitrarily fine spatial resolution. We introduce a
screening length parameter, $L_{\rm res}$, proportional to the inverse of the
local temperature in the plasma, estimating a range for the value of the
proportionality constant via comparing weakly coupled QCD calculations and
holographic calculations appropriate in strongly coupled plasma. We then modify
the hybrid model so that when a parton in a jet shower splits, its two
offspring are initially treated as unresolved, and are only treated as two
separate partons losing energy independently after they are separated by a
distance $L_{\rm res}$. This modification delays the quenching of partons with
intermediate energy, resulting in the survival of more hadrons in the final
state with $p_T$ in the several GeV range. We analyze the consequences of
different choices for the value of the resolution length, $L_{\rm res}$, and
demonstrate that introducing a nonzero $L_{\rm res}$ results in modifications
to the jet shapes and jet fragmentations functions, as it makes it more
probable for particles carrying a small fraction of the jet energy at larger
angles from the jet axis to survive their passage through the quark-gluon
plasma. These effects are, however, small in magnitude, something that we
confirm via checking for effects on missing-$p_T$ observables.
