Transneuronal degeneration: atrophy of certain neurons after interruption of afferent axons or the death of other neurons to which they send their efferent output.

Basically means that the death of one neuron causes atrophy or death in the the neurons in it's forward path of connection (the neurons it stimulates). A neuron's metabolism is regulated by the amount of stimulation it gets, if no stimulus is received, it degenerates. Known colloquially as the Use it or Lose it mechanism.

I'm not sure which diseases that would include, probably a lot of them. But while out searching I found something thought was interesting in light of the progression of Lewy Bodies in PD:

The Vagus Nerve is One Route of Transneural Invasion for Intranasally Inoculated Influenza A Virus in Mice