You have just raised a new question not present in the first, of notifying possible claimants.
I am not aware that there is a claim merely for being exposed to asbestos*. If you get mesothelioma or another asbestos related disease, then yes, there is a claim.
* "Damage" is an essential ingredient of a claim. No damage, no liability. Remember the tort lawyer's checklist: duty; breach; causation; damage.