Exposure to asbestos confers a long-term risk of developing pleural and peritoneal mesothelioma which increases following cessation of exposure. While the rate of increase appears to start to level out after 40-50 years no one survives long enough for the excess risk to disappear.

 2014 May 19. pii: thoraxjnl-2013-204161. doi: 10.1136/thoraxjnl-2013-204161. [Epub ahead of print]
Mesothelioma risk after 40 years since first exposure to asbestos: a pooled analysis.