So Will is sent out to find Jack and Elizabeth is left her cell with a bunch of weirdos. "Keep a weather eye on the horizon." -Will. Eventually, her father comes to sneak her out of jail. He plans on secretly sending her to England before anything worse happens. Beckett's men hear of her escape and track down her wagon. Elizabeth was too smart for them and fled before they cornered it. Soldier: "Where is she?" Governor Swann: "Who?" Who do you think they're asking you about?
Elizabeth sneaks into Cutler Beckett's office. Beckett: "No doubt you've discovered that loyalty is no longer the currency of the realm, as your father believes." Elizabeth: "Then what is?" Beckett: "I'm afraid currency is the currency of the realm." Obviously. Elizabeth: "I"m hear to negotiate." Beckett: "I'm listening." Then, as all pirates do, she holds a pistol to his face. "I'm listening intently." She then goes into this big rampage about how he doesn't really want the compass because it will do him no good. She thinks it will take him the Isla de Muerta only to find the cursed Aztec gold. That's when she realizes, the compass doesn't just point to the island, it will point anywhere, to anything you want the most. I guess she will need to find a better persuasion tactic. That's where the pistol comes in handy again. Elizabeth: "Consider into your calculations that you robbed me of my wedding night." Beckett: "I'll still want that compass. Consider that in your calculations." She then runs out of the office with the signed letters of Mark to the king that now bear Beckett's signature. She climbs on board a ship and leaves Port Royal for the rest of her life.