New arrivals to Hyperion are greeted with a statue of Sad King Billy. It's nothing exciting. In his journal, Father Duré writes that it "was oddly disappointing" (1.184), and the same might be said about the man himself.
Martin Silenus travels with Sad King Billy, whom he says "looks a bit like a wax candle of a man who has been left on a hot stove" (3.233). (Ouch.) They're some of the first settlers on Hyperion, which is supposed an artist's mecca for painters, sculptors, poets, and artists alike. Billy brings Silenus along because he was one of the only people who appreciated Silenus's Cantos.
Billy wants Silenus to continue writing. In that sense, he's like a king who keeps artists in his court for his own amusement. But notice that we said like. Billy's actually kind of a pathetic figure who collects artists because he can't create anything on his own: "King Billy is the fat child with his face eternally pressed to the candy store window. He loves and appreciates fine music but cannot produce it" (3.238).
Sad King Billy has an air of Billy Pilgrim about him, from Kurt Vonnegut's Slaughterhouse-Five, a man unstuck in time and trying to find his place. He meets a much more gruesome fate though, one tinged with irony, as the Shrike, allegedly summoned by the Cantos Billy implored Silenus to finish, slaughters him in the middle of the Poet's City.