I think SQuAD 2.0 introduced this kind of “unanswerable” questions:

  
      
      arXiv.org
  
  
    

Know What You Don't Know: Unanswerable Questions for SQuAD 14

Extractive reading comprehension systems can often locate the correct answer
to a question in a context document, but they also tend to make unreliable
guesses on questions for which the correct answer is not stated in the context.
Existing datasets...


  
  
    
    
  
  


Demo on the model hub that uses a fine-tuned model:
https://huggingface.co/deepset/bert-base-cased-squad2?text=Where+lives+Wolfgang%3F&context=My+name+is+Wolfgang+and+I+live+in+Berlin 19
Outputs “Berlin” correctly. Now an unanswerable question (because it is not given in the context):
https://huggingface.co/deepset/bert-base-cased-squad2?text=Where+was+Obama+born%3F&context=My+name+is+Wolfgang+and+I+live+in+Berlin 18