Within the scope of this thesis, we show that a driven-dissipative system with few ultracold atoms can exhibit dissipatively bound states, even if the atom-atom interaction is purely repulsive. This bond arises due to the dipole-dipole interaction, which is restricted to one of the lower electronic energy states, resulting in the distance-dependent coherent population trapping. The quality of this already established method of dissipative binding is improved and the application is extended to higher dimensions and a larger number of atoms. Here, we simulate two- and three-atom systems using an adapted approach to the Monte Carlo wave-function method and analyse the results. Finally, we examine the possibility of finding a setting allowing trimer states but prohibiting dimer states. In the context of open quantum systems, such a three-body bound states corresponds to the driven-dissipative analogue of a Borromean state. These states can be detected in modern experiments with dipolar and Rydberg-dressed ultracold atomic gases.