As noted by others, living with chronic pain is a whole other animal from treating and rehabbing an acute injury, or from learning to differentiate, on the mat, between essentially benign pain you can relax into (a good pin for example) and pain that signals imminent damage.
The person with chronic pain will likely have good and bad days or even hours, so may seem very inconsistent in the level of training he can tolerate. It does not mean he is lazy or not serious about training.
The person with chronic pain will likely have a highly developed sense of distinguishing between "benign pain" and pain that signals "stop" (my dojo mates know not to grab or hold my thumbs - but I know that if the grab or hold is momentary, while it will hurt like the dickens and I may screech, it is unlikely to actually do further damage).
The most important skill a person with chronic pain can cultivate, IMO, is to learn to accept and integrate the pain as an part of his life: if it is perceived as an entity separate from the person, something to be battled, it actually empowers the pain more than it merits and, paradoxically, can become self-defining. When it is an integral part of life, along with all the other quirks, traits, strength, weaknesses, preferences, etc that comprise a human being, it becomes simply another thing to factor into daily life.