Can a third party ask for an annulment if neither married person wants it to happen? Say that a couple was married despite an impediment, which is usually justification for annulment. Some examples of impediments include:


One of them was abducted (raptus, or bride kidnapping) and has been under the kidnapper's control since to the point of developing Stockholm syndrome. 
The two are close blood relations and there is an issue of consanguinity. 


Now let's say that both married people do not wish to have their marriage annulled. Can a third party, such as their families, ask for an annulment?
Yes, it's possible, but Canon Law provides a specific method:


  
  The following are qualified to challenge a marriage:
  
  
  the spouses;
  the promoter of justice when nullity has already become public, if the convalidation of the marriage is not possible or expedient.
  
  
  
  [CIC]


For a marriage to be challenged, the family must first prove the nullity in public (for example, criminal bigamy, or lack of consent, or prohibted consanguity) which would prove the marriage civilly invalid, and then present the promoter of justice with that evidence for him to petition the Marriage Tribunal for sacramental nullity.

The promoter of justice is "the person appointed in each diocese and in the higher tribunals of the Catholic Church whose responsibility it is to provide for the public good." The relevant tribunal will be able to identify the particular person in its case.