Played around with a mesh from somebody else trying to pose it to test the MeshDeform modifier. For this I made a simple cage around the body, arms and head. It encloses the mesh with a bit of space as it should be with such a cage. Now what happens is that parts of the body does deform if the cage deform. But for some reason the entire head and arms do not move. I tested it also with other meshes from myself and the MeshDeform only works sometimes. Is there anything wrong with the MeshDeform modifier or does it have some strange limitations one should know? The cage mesh is properly made enclosing the model as a manifold closed mesh.
Figured it out. Faces require normals to point to the outside, not the inside.