There is a difference in fractured and broken. Broken is more severe. A fracture is basically a "crack" in the bone. Taping can help the person stay mobile if done appropriately. This is true about many injuries. I was a coach who had to take lots of biology, anatomy, kinesiology, care and prevention of athletic injuries, first aid, CPR, etc.
I have gotten many people to the ER and have had the doctors there brag on what I've done. I have stopped a whole lot of incorrect frist aid from happening also. Poor initial treatment can cause more damage. Poor taping can help or create worse problems. Continuing to tape too long can also hinder healing. One continual piece of tape can create improper circulation. (This can create more pain also - so maybe you can use that somehow.) Knowing how to tape specific injuries is a huge deal!
I know that any ailment with the lungs is painful. Even Pluerisy which is an inflamation of the pluera sack that surrounds the lungs is extremely painful. You can be O.K. one second and then next you are immobolized due to knife-like pain and you feel like you have to "sneek" a breath in due to the pain.
So, I don't know your storyline, but this could work for being able to use the ailment to your advantage. He could do "stuff" but then at times, he would be in too much pain. I know, this personally, as a tennis coach who has had it more than once. I could feed drills for a little bit and then be lying on the court in pain. The pain can also move around to different areas very unexpectantly.
Hope my rambling might have given you something to use.
*Also, please excuse all the errors, I'm sure you will find in spelling, etc. I was just rushing to give a few ideas and I am too lazy to proof it! LOL!