Asbestos claims, long considered an ever-expanding problem for property-casualty insurers, have declined recently as a result of reform efforts–but that doesn't mean insurers can stop worrying about their reserves, experts warn.

“We're seeing a significant change in asbestos litigation,” said Faten Sabry, a vice president with NERA Economic Consulting in New York.

Specifically, Ms. Sabry pointed to two phenomena fueling the change–a series of asbestos tort reforms passed in several states, and a ruling last year by U.S. District Court Judge Janis Graham Jack in the Southern District of Texas, Corpus Christi, in a silica multidistrict suit that sharply criticized the practices of some law firms and those they hired to screen potential plaintiffs for asbestosis.