Eg. if a person dies of lung cancer, then we roll a dice and say "theres a 1 in 6 chance that was due to pm2.5 emissions". If the dice rolls a 1, then we look around the town for sources of pm2.5, and we find that 1/6 comes from a candle factory. We roll another dice, and if that comes out with a 1, then we say "This factory emitted air pollution that killed this person".
Then we treat it in law exactly the same as if the person had walked by the factory and been decapitated by a piece of roof falling off. Ie. we let the family sue. We send inspectors to see if there is negligence involved, etc.