Yes they are called senescent cells and removing them seems to have an anti-ageing effect.

All our cells (not just nerve cells) communicate chemically with each other to a certain degree.

One of the theories of ageing is that these senescent cells are able to cause disease and ill health without becoming cancerous, probably by releasing certain chemical agents which act to cause dysfunction in otherwise normal cells.

They seem to ratchet up the activity of the immune system in particular which can cause chronic inflammation - another process that seems to increase with age and also acts to cause damage to healthy cells, potentially causing a feedback loop which creates more senescent cells.

Under normal circumstances such cells are supposed to commit suicide by a process known as apoptosis (programmed cell death). However as we age these processes seem to get less efficient (possibly due to DNA damage) and we slowly build up more and more of them.

So to summarise they act lack bad leaders which signal other cells to misbehave and once they are removed the other cells go back to functioning normally.

I believe combining this sort of therapy to remove senescent cells and supplementing stem cells would create a very potent means of rolling back the chronological clock.