go the way of the dodo vs run out

go the way of the dodo

verb
  • To go extinct or become obsolete; to fall out of common practice or use; to become a thing of the past. 

run out

verb
  • To expire; to come to an end; to be completely used up or consumed. 

  • Used other than figuratively or idiomatically: see run, out. 

  • To extend a piece of material, or clothing. 

  • To get a batsman out via a run out (see runout) 

  • To use up; to consume all of something. See also run low, run short. 

  • to be got out in this way. 

  • To conclude in, to end up 

  • To force (someone or something) out of a location or state of being. 

How often have the words go the way of the dodo and run out occurred in a corpus of books? (source: Google Ngram Viewer )