Thank you for your post to the message board.
I assume that this is the family that you are referring to in the 1901 Census:
I did not see a death record for Michael O'Connor, but it is possible that Honour did die between 1901-1911, or that she possibly may have emigrated with one of her children.
Honour O'Connor, the daughter may also have emigrated. Have you check the Clare Library website? They have transcriptions for passengers and other resources that may assist you. I will ask locally to see if any member of the family remained and if there are descendants in the area.
The Clare Library website is: http://www.clarelibrary.ie/eolas/coclare/genealogy/genealog.htm
You can also contact me directly at: email@example.com.
All the best,