Just because it's been years since you handled or worked around asbestos doesn't mean you don't have a claim against the manufacturer and other people who told you it was safe. Mesothelioma, an illness almost exclusively associated with asbestos, has a latency of up to 50 years. If you're diagnosed with Mesothelioma, it's time to look for an attorney.
Billions of dollars have been set aside to pay the victims of asbestos-based Mesothelioma and related illnesses, even though the companies that made the materials have long since been forced into bankruptcy. Don't think there's not enough of the pie to give you a substantial slice; if you've got a valid claim, you should file it.