The Devil finds work for idle hands. My paternal grandmother who worked all her life running a guest house.

It's not the cough that carries you off
It's the coffin they carry you off in.

No, I've still no idea what it means.

[Botherer] My father said that as well, and I've met other people who recognised it. Google has "about 57,000" hits for the complete saying in quotes (but only "about 13,200" without quotes).

My parents and wife have all used that one.

I think he's studying to be an idiot. Said by father about any school-aged person he thought was a twat.

Is anyone still listening?

I heard that, pardon - as my parents used to say, which I've just googled to discover it's from "I Didn't Know You Cared", which I didn't know was written by Peter Tinniswood.
[Raak] I don't think so, TBH.