Short answer
Yes.
Background
Notable examples of this happen in in the peripheral sensory systems. There, marked degenerative processes are present when input to the secondary neurons is lost due to degeneration of the primary sensory neurons. In other words
- When the hair cells are lost in the cochlea, the auditory nerve degenerates (*e.g., Kuyama, 2010);
- When the retinal photoreceptors are lost, for example due to degenerative diseases like retinitis pigmentosa, bipolar and horizontal cells in the retina degenerate due to a loss of efferent input (Mazzoni et al., 2008). For more information see the works of Marc & Jones, e.g.., (Jones & Marc).
Note that in the central nervous system these effects play less of a role, as neurons have ample opportunity to reconnect to other neurons, for the better or worse; e.g., in the hearing and visual impaired spontaneous sensations of sound and visuals may develop and lead to tinnitus and photopsias, respectively.
References
- Jones & Marc, Exp Eye Res (2005); 81(2): 123-37
- Kuyama, J Neurosci (2009); 29(45): 14077–085)
- Mazzoni et al., J Neurosci (2008); 28(52): 14282–92