  This paper presents a novel model for bivariate stochastic fluid processes
that incorporate a ruin-dependent behavioral switch. Unlike typical models that
assume a shared underlying process, our model allows each process to operate
independently until a ruin event in one triggers a change in the other. We
develop a mathematical framework for our model, exploring its properties and
providing closed-form expressions for approximations of key performance
metrics, particularly the joint law of the ruin times. Our approach introduces
a class of compatible pathwise approximations to analyze ruin probabilities,
which we subsequently study through a matrix-analytic framework.
