Units of Travelers Cos. Inc. and American International Group Inc. that had provided excess coverage to a now-bankrupt asbestos manufacturer are not obligated under their policies' terms to provide coverage until primary insurers have paid in full under their policies, Business Insurance reported yesterday. Rapid-American Corp., which started getting sued for asbestos-related personal-injury claims in 1974, settled many of the claims by the time it filed for chapter 11 in March 2013, but it still had about 275,000 asbestos-related personal-injury claims pending against it at the time.