Good question. I have no knowledge of asthma leading to cancer. However, in some instances asthma can lead to COPD. Usually severe, persistent asthma is considered COPD. This happens when asthma gets so bad that it causes airway changes, such as airway scarring. This will result in chronic airway obstruction that would be considered a COPD condition.
How can this happen? One way it can happen is poorly controlled asthma. This can result in airway changes. Yet another way is if you smoke. I'm not sure what the statistics are, yet I believe asthmatics who smoke are at an increased risk for developing chronic airway changes.
To prevent this, you will want to make sure asthma is diagnosed promptly and treated aggressively. You must be a gallant asthmatic, see your doctor regularly and take all your medicine as prescribed.