  The article deals with existence and uniqueness of the solution of the
following differential equation (a c\`adl\`ag Skorokhod problem) driven by a
maximal monotone operator and with singular input generated by the
c\`{a}dl\`{a}g function $m$: \[ \left\{ \begin{array} [c]{l} dx_{t}+A\left(
x_{t}\right) \left( dt\right) +dk_{t}^{d}\ni dm_{t} \,,~t\geq0,\\ x_{0}=m_{0},
\end{array} \right. \] where $k^{d}$ is a pure jump function. The jumps outside
of the constrained domain $\overline{\mathrm{D}(A)}$ are counteracted through
the generalized projection $\Pi$, by taking $x_{t}=\Pi(x_{t-}+\Delta m_{t})$,
whenever $x_{t-}+\Delta m_{t}\notin\overline {\mathrm{D}(A)}\,$. Approximations
of the solution based on discretization and Yosida penalization are considered.
