Is there a disease or condition that destroys nerve cells

Multiple sclerosis is an inflammatory disease in which the fatty myelin sheaths around the axons of the brain and spinal cord are damaged, leading to demyelination and scarring as well as a broad spectrum of signs and symptoms. Disease-modifying treatments reduce the progression rate of the disease, but do not stop it. As multiple sclerosis progresses, the symptomatology tends to increase. The disease is associated with a variety of symptoms and functional deficits that result in a range of progressive impairments and disability. Management of these deficits is therefore very important. Both drug therapy and neurorehabilitation have shown to ease the burden of some symptoms, though neither influences disease progression.

Autoimmune diseases (of which there are a wide range) target human cells, mistakenly identifying them as threats to the body. They can attack nerve cells.
Another disease, known as Huntington's, causes cells of the spine and brain to deteriorate. It is a genetic disease.