Studies show the unhappy reality of dysfunctional behaviors often being passed down through generations. As human beings, we tend to repeat the behaviors that were done to us, even when we don't want to. This is fairly common knowledge, so it stands to reason that a character who suffered abuse would fear the possibility of  perpetuating habits they view as abhorrent and destructive. While their intentions may be good, their fear may drive them to extremes or to ineffectual methods that are harmful in their own way. 

Not having children
Avoiding intimate relationships
Resisting vulnerability with others (to avoid being mistreated again)
Needing to control every aspect of life
Being highly disciplined
Attending therapy to come to terms with the past
Abstaining from drugs and alcohol, since addiction is often tied to abuse
The character spoiling their children so they never will experience neglect
Being so involved in a child's life that they feel smothered
Being too permissive
The character putting everyone else's needs above their own
The character cutting ties with their own abuser
Choosing not to forgive an abuser (so the character can maintain a perspective that will keep them from repeating that behavior)
Withdrawing often (to deal with intrusive thoughts in private or to keep others safe)
Hiding past abuse