run its course vs sign off

run its course

verb
  • To come to a natural end. 

sign off

verb
  • to give one's official approval to something for which it is needed 

  • To log off; to stop using a computer, radio, etc., especially to stop talking. 

  • To cease broadcasting a radio or television signal, usually at the end of a broadcasting day. 

noun
  • The closing of a radio or television station's studios and cessation of the broadcasting signal, usually overnight. 

How often have the words run its course and sign off occurred in a corpus of books? (source: Google Ngram Viewer )