We consider the scenario of an emitter embedded in a nonideal cavity, accounting for the possibility that the emitter and cavity photons interact with a common photonic environment. Using an inputoutput approach to describe the open system, we demonstrate that this situation gives rise to an effective dissipative coupling between the emitter and the cavity. The underlying mechanism is independent of the nature of the emitter and exists even at zero temperature; hence our results are potentially relevant for a variety of experimental platforms. We show that the effective dissipative coupling can lead to physical effects that do not occur in closed light-matter coupled systems. In particular, when the radiative decay rates exceed the conventional Rabi coupling, we can have the phenomenon of level attraction between the emitter and cavity mode. Our model thus provides a possible explanation for the level attraction observed in recent photoluminescence measurements in semiconductor microcavities. Finally, we demonstrate that hybrid light-matter exceptional points and bound states in the continuum can be realized within this model.