Particles with purely repulsive interactions do not undergo phase separation in equilibrium. However, when driven out of equilibrium by self-propulsion, such particles can aggregate despite the absence of attractive forces, leading to motility-induced phase separation (MIPS). By studying the differences between MIPS and equilibrium phase separation, we have recently gained much insight into the unique features of macroscopic behaviors in nonequilibrium systems. In this talk, I will highlight one such difference: the stability of MIPS and equilibrium phase separation in quenched disorder. Specifically, it will be shown that MIPS is relatively unstable in quenched disorder and its stability depends on boundary conditions, unlike equilibrium phase separation which remains unaffected by boundary conditions. This behavior arises from the absence of time-reversal symmetry and can be generalized to a wide range of nonequilibrium models.