Continental Casualty Co. v. Rapid-American Corp. (1993) established that insurers must defend policyholders against asbestos exposure claims even when injuries appear after the policy period ends. The court ruled that pollution exclusions don't apply to occupational asbestos inhalation injuries. An insurer's duty to defend is triggered whenever a complaint reasonably suggests coverage is possible, based on the complaint's language alone. This matters to subcontractors because it clarifies that your general liability insurance should cover asbestos-related claims from work performed during the policy period, regardless of when symptoms develop.
Your insurer must defend you if the complaint alleges any reasonable possibility of coverage—they can't deny defense based on their interpretation of policy language alone.
Asbestos exposure claims from occupational work are not blocked by standard pollution exclusions, so your CGL policy should provide coverage for these claims.