Are idioms like 亡羊补牢 commonly used by native Mandarin speakers?
Some Chinese idioms are special, it depends on the sentences context and the say you express it. 

This is the complete idioms  


  亡羊而补牢，未为迟也。(if is never too late if you fix the fence immediate after the first few sheep escape. ) 


When one say 亡羊补牢, it can either mean : 


  i. To comfort or remind someone that it is not too late to fix the mistake, or
  
  ii. Somebody mess up in the first place, now they are fixing it. 
  
  iii. A hint that somebody make a mistake that must be fixed.


This is why Chinese don't simply throw out the idiom 亡羊补牢 unless you are pretty sure what you mean.