--there is no response at all in certain areas, that would point to the destruction of the cell body and the entire nerve. But that is vanishingly rare.

Often, certain cells in an area have died, but since nerve are made up of so many cells and fibers others will pick up enough of the slack that there will still be some response.

Other than that, one can have biopsy material examined microscopically and observe dead cells, but I've never heard of a situation in which all of the cells from a sample were dead.

There are certain conditions in which it is thought the soma is preferentially damaged--these are often referred to as "neuronopathies" though symptomatically it may be hard to distinguish them from neuropathies. A number of these seem to be characterized by cell body destruction in the dorsal root ganglia:

Sensory Neuronopathies