  The derivative discontinuity in the exact exchange-correlation potential of
ensemble Density Functional Theory (DFT) is investigated at the specific
integer number that corresponds to the maximum number of bound electrons,
$J_{max}$. A recently developed complex-scaled analog of DFT is extended to
fractional particle numbers and used to study ensembles of both bound and
metastable states. It is found that the exact exchange-correlation potential
experiences discontinuous jumps at integer particle numbers including
$J_{max}$. For integers below $J_{max}$ the jump is purely real because of the
real shift in the chemical potential. At $J_{max}$, the jump has a non-zero
imaginary component reflecting the finite lifetime of the $(J_{max}+1)$ state.
