Assuming that most of the "workers" on the death star were clones, there wouldn't be any need to pay the families. I'm sure that Palpatine was wise enough to make them sign waivers against liability. Chances are, those families probably sued the designers of the Death Star, because they were the ones who designed the fatal flaw. I'm sure there were all kinds of hearings to find out the source of the leak who gave the plans to the rebels, as well. Luckily, the Emperor had used is Sith power of foreknowledge and took out a large enough insurance policy with a "Rebel Alliance" clause. This is evidenced by the fact that he got funding to build a second Death Star. His premiums probably shot through the roof after that, though. When the second Death Star was destroyed, none of the remaining underwriters were willing to take his claim as the original was bankrupt by the two massive payouts for both destroyed Death Stars.