The envelope of the red supergiant VY CMa has long been considered an extreme example of episodic mass loss that is possibly taking place in other cool and massive evolved stars. Recent (sub-)millimeter observations of the envelope revealed the presence of massive dusty clumps within 800 mas of the star and reinforce the picture of drastic mass-loss phenomena in VY CMa. We present new ALMA observations at an angular resolution of 0.1'' and at an unprecedented sensitivity that reveal further details about the dusty clumps. We resolve more discrete features and identify a submillimeter counterpart of a more distant Southwest (SW) Clump known from visual observations. The brightest clump, named C, is marginally resolved in the observations. Gas seen against the resolved continuum emission of clump C produces a molecular spectrum in absorption, in lines of mainly sulfur-bearing species. Except for SW Clump, no molecular emission is found to be associated with the dusty clumps and we propose that the dusty structures have an atypically low gas content. We attempt to reproduce the properties of the dusty clumps through 3D radiative transfer modeling. Although a clump configuration explaining the observations is found, it is not unique. A very high optical depth of all clumps to the stellar radiation makes the modeling very challenging, and requires an unrealistically high dust mass for one of the clumps. We suggest that the dusty features have substructures (e.g., porosity) that allow deeper penetration of stellar photons within the clumps than in a homogeneous configuration. A comparison of the estimated clump ages to variations in the stellar visual flux for over a century suggests that the mechanism responsible for their formation is not uniquely manifested by enhanced or strongly diminished visual light. The study demonstrates that the dusty mass-loss episodes of VY CMa are indeed unparalleled among all known non-explosive stars. The origin of these episodes remains an unsolved problem.