At this point: almost no one. The super majority of manufacturers and distributers of asbestos products have gone bankrupt. Kaiser Gypsum was one of the last solvent companies involved in a lot of asbestos litigation and they filed for bankruptcy a few years ago. Bankrupted companies of this kind generally establish trust funds for claims related to asbestos products, but those funds pay out paltry amounts. There are a few other large solvent companies though, so it depends on what caused the likely exposure. If, like many people, a person got asbestosis or mesothelioma while in the armed services, they are SOL because the VA pays squat.
In Australia, there are Government backed, employer funded workers compensation funds that will cover this. You can also sue the makes of the product as well.
In my grandfathers case, he successfully sued a company called "James Hardie". It's a slam-dunk case. They confirm that you would have been exposed to the product and then it's a mathematical equation to determine the claim value.
