The disease is mesothelioma (hope that's spelt correctly), and it's caused by the microscopically fine fibres of asbestos, especially blue asbestos, penetrating the mesothelium, which the Macquarie Dictionary defines as the "epithelium of mesodermal origin which lines the body cavities" especially the lungs.

There was a long battle for compensation between the mining company and the men who contracted the disease. The less charitable might say that the mining company dragged it out as long as they possibly could so that more of the claimants could die before they collected, but surely no reputable company could take that approach?