fail vs remain

fail

verb
  • To neglect. 

  • Not to achieve a particular stated goal. (Usage note: The direct object of this word is usually an infinitive.) 

  • To become unable to meet one's engagements; especially, to be unable to pay one's debts or discharge one's business obligation; to become bankrupt or insolvent. 

  • To receive one or more non-passing grades in academic pursuits. 

  • To give a student a non-passing grade in an academic endeavour. 

  • To be wanting to, to be insufficient for, to disappoint, to desert; to disappoint one's expectations. 

  • To be wanting; to fall short; to be or become deficient in any measure or degree up to total absence. 

  • To be unsuccessful. 

  • Of a machine, etc.: to cease to operate correctly. 

noun
  • A failure, especially of a financial transaction (a termination of an action). 

  • A failure (condition of being unsuccessful). 

  • A failing grade in an academic examination. 

  • Poor quality; substandard workmanship. 

  • A failure (something incapable of success). 

  • A piece of turf cut from grassland. 

adj
  • Unsuccessful; inadequate; unacceptable in some way. 

remain

verb
  • To await; to be left to. 

  • To continue in a state of being. 

  • To continue unchanged in place, form, or condition, or undiminished in quantity; to abide; to stay; to endure; to last. 

  • To be left after a number or quantity has been subtracted or cut off; to be left as not included or comprised. 

  • To stay after others or other parts have been removed or otherwise disappeared. 

noun
  • That which is left; relic; remainder. 

  • That which is left of a human being after the life is gone; relics; a dead body. 

  • Posthumous works or productions, especially literary works. 

How often have the words fail and remain occurred in a corpus of books? (source: Google Ngram Viewer )