You know, I've been wondering when Death changed. Gaiman showed a character progression; in Endless Nights, she was melodramatic and into ballgowns and a little sadistic and depressed. Nobody liked her or wanted her around.
Modern times, she is perky and philosophical and even cheery about what she offers. It would make sense that Xanadu, a master of symbolic magic, offered Death a choice: be the feared End of Life that she'd always been, or take on the new meaning that Xanadu described. She literally bargained for immortality in exchange for a paradigm shift.