  The effect of particle-nonconserving processes on the steady state of driven
diffusive systems is studied within the context of a generalized ABC model. It
is shown that in the limit of slow nonconserving processes, the large deviation
function of the overall particle density can be computed by making use of the
steady state density profile of the conserving model. In this limit one can
define a chemical potential and identify first order transitions via Maxwell's
construction, similarly to what is done in equilibrium systems. This method may
be applied to other driven models subjected to slow nonconserving dynamics.
