Shouldn't have to explain this power you can't die. However I will say this immortals are not invinicble they can still feel pain. Which is why I choose Hidan as my example, sure he can't die but he feels pain and if he gets a limb chopped of he can't do anything unless his partners sews it back on for him. (People who watch Naruto will know what I'm talking about)
So yeah there is a lot of debate on whether or not this is a good power. (Personally I like the way Baccano displays the power. I also like the Elves from The Lord of the Ring series, they can't die via natural causes, but they can die in battle. At least I think that's how it goes, if I'm wrong please correct me.)