By default, Mmg considers only boundaries that are delimiting the mesh (external boundaries) or that are at the interface between two different domains (internal boundaries). Thus, if the user provide a portion of surface that is not at the interface between two domains with different references (see figure 1, mesh island.mesh), by default, this surface is deleted.
If you want to preserve an open boundary, you have to run Mmg in
opnbdy mode. You can see on the figure 2 the result of the remeshing of the previous mesh using the following command line:
mmg3d_debug -opnbdy island.mesh
We can see that the open boundary is not deleted and is remeshed at the same time than the volume mesh.
Note that it slows down the code so when a boundary shares a domain into 2 distinct domains, it is better to assign different references to each domain and to run Mmg as usually than to use the -opnbdy option.