Surely the prime superstition, as found in Henry Clay Work's My Grandfather's Clock, which was

...bought on the morn of the day that he was born
It was alsways his treasure and pride
But it stopped, short, never to go again
When the old man died

is that the clock will cease to function on its owner's death. I remember, at the climax of the film of Pushkin's The Queen Of Spades, when a loud ticking on the sound track stops at the moment the old countess (Edith Evans IIRC) snuffs it.

~Michael~