It's comforting to know that the majority of people with chronic pain do not become addicted to pain medication or, as a substitute, illegal drugs. There are risk factors that can predispose a person to addiction/dependency issues such as either a family history or personal history of substance abuse/addiction, being a smoker, preadolescent sexual abuse, personal psychiatric history.
Medscape article Management of Chronic Noncancer Pain in the Primary Care Setting from 2007
PubMed article What percentage of chronic nonmalignant pain patients exposed to chronic opioid analgesic therapy develop abuse/addiction and/or aberrant drug-related behaviors? from 2008 explain this complex issue.
The Medscape article also highlights the need to avoid undertreating pain and does not favour this as an alternative! It states that undertreating pain can cause a patient to display addiction like behaviours, such as aggression.
I have always thought that a person with chronic pain is less likely to develop problems because they know their pain is going nowhere so they can't afford to speed up the journey to tolerance because they could be left with their pain and no alternatives. Someone with acute pain could play fast and loose with their medication knowing they won't still need it next week, month or year whereas the person with chronic pain can't afford to do this.