In an attempt to resolve this problem, Senator Arlen Specter introduced S. 852 , the Fairness in Asbestos Injury Resolution (FAIR) Act. The Claims Process

The bill would establish within the Department of Labor the Office of Asbestos Disease Compensation, which would award damages to claimants on a no-fault basis according to their respective levels of injury and asbestos exposure. For claimants who have asbestos claims pending in court, the statute of limitations would be five years from enactment of the bill. The Asbestos Injury Claims Resolution Fund

The Fund would be paid for by contributions from defendants in asbestos suits – "defendant participants" – and their insurers – "insurer participants."
This report provides an overview of S. 852, the Fairness in Asbestos Injury Resolution (FAIR) Act of 2005. The bill would largely remove asbestos claims from the courts in favor of the no-fault administrative process set out in the bill. The bill would establish the Office of Asbestos Disease Compensation to award damages to asbestos claimants from the Asbestos Injury Claims Resolution Fund. Companies that have previously been sued for asbestos-related injuries—and insurers of such companies—would be required to make contributions totaling roughly $140 billion to this Fund.