The purpose of PBCs is to eliminate surface effects. However, we may also be interested in situations where we want to have surfaces. Obviously, all surface physics problems belong to this class!
For a surface simulation, the model usually adopted is that of the slab: a thick slice of material, delimited by two free surfaces. This is simply obtained by removing PBCs along one direction (usually taken to be z) while retaining them in the orthogonal plane. Therefore, a slab must be thought as replicated to infinity in the xy plane, but there is no replication along the slab normal z.
If the slab is thick enough, its inner part is expected to be quite similar to the bulk of the material. The two surfaces (at the top and at the bottom of the slab) can then be thought of as two decoupled, independent surfaces. With this assumption, the system behavior would be close to that of a single surface at the top of a semiinfinite system--a condition which would be closer to actual surface experiments but which is unfortunately impossible to realize in simulation.
There are also circumstances where researchers find it preferable to ``freeze'' a few layers of material at one side of the slab--with the atoms constrained to sit at perfect bulk-like crystal positions--leaving only the other side free. This is done when it is believed that spurious effects induced by the frozen side into the ``good'' side of the slab are of smaller entity than the effects induced by another free surface at the same separation distance. This is to be preferred in those cases where massive perturbations occur at the surface, such as atomic rearrangements (surface reconstructions) or local melting. If a slab with a frozen side is chosen, care must be taken to freeze a number of layers corresponding to a thickness of at least Rc, to guarantee that no mobile atom would be able to ``see'' the surface ``through'' the fixed atoms.
One can also leave PBCs along only one direction only, thus obtaining a wire geometry with the wire axis along the PBC direction, or remove them altogether. This latter condition correspond to a cluster of atoms. Clusters are important systems and simulation of clusters have been performed since the early days of molecular dynamics and Monte Carlo.