Final answer:
The mesencephalic nucleus is the proprioception nucleus for the face, and proprioceptive input from the upper and lower trunk and limbs is processed by the dorsal column system, with input to the cerebellum from the medulla or inferior olive respectively.
Step-by-step explanation:
The nonconscious proprioception nucleus corresponding to the cerebellum for the face is the mesencephalic nucleus of the trigeminal nerve. For the upper trunk and limbs, proprioceptive information enters the cerebellum through collateral projections of the dorsal column system that synapse in the medulla. In contrast, for the lower trunk and limbs, proprioceptive sensations are similarly processed through the dorsal column system, and conveyance to the cerebellum occurs via collateral projections to the inferior olive and then to the cerebellum.
The cerebellum's role in the motor system is vital as it integrates and compares cerebral motor commands with proprioceptive feedback to ensure coordinated movements. Issues with proprioception or execution of motor commands are resolved through the cerebellum's comparison and subsequent sending of corrective signals via the rubrospinal tract.