There are a few ways to end up in this group, and to be honest, none of them are very fun. If you're like Eurydice, you die before your time. But there are other methods, too: say, being kidnapped or going on an ill-advised adventure into the land of the dead. No matter how you manage to fall in with this clique, it's one group from which there's just no way out.
Like Eurydice, Persephone was a pretty young thing when she was taken to the Underworld. Persephone didn't get there by dying, though—since she's a goddess, that would be impossible. Instead, she was kidnapped by her uncle Hades, and forced to be his queen. We've got the whole scoop for you.
Pirithious was BFF of the Athenian hero, Theseus. He ended up trapped in the Underworld after he came down, accompanied by Theseus, to take Persephone away as his wife. Hades didn't take too kindly to this and trapped Pirithious in the Underworld for good.
This Japanese goddess ended up in the Underworld after dying in childbirth. Her husband, Izanagi-no-Mikoto, went down to bring her back to the world of living, but just like Orpheus, he wasn't able to complete his quest. Like Persephone, Izanami-no-Mikoto had eaten the food of the Underworld and was trapped there. When her husband shined a light on her, he saw that she was a rotting corpse covered with maggots. Then she went all zombie on him and chased him out of the Underworld.