We construct and analyze a system of stochastic differential equations satisfied by the position and the diffusion coefficient of a Brownian particle whose diffusion coefficient is modified at each crossing of the origin and with a dumping coefficient. This system models the effects of lipid accumulation on macrophage dynamics. The novelty of the model, with respect to [1, 15], is to include offloading of lipids through the dumping term. We obtain non-trivial behaviors of the solution: dynamical transition to an absorbing state for the solution to the stochastic system. With this model, we study how changes in parameters, initial conditions included, predict some characteristic features of plaque pathology, which in our case is described by macrophage aggregation.