In King Lear, Cordelia leaves the kingdom because her father, King Lear, banishes her.
In the play's opening scene, King Lear approaches his three daughters and asks them to display their love towards him. The first two daughters, Regan and Goneril, make dramatic and elaborate scenes of their affections. When it is Cordelia's turn, she breaks from her sisters and refuses to participate in such a public display. With statements such as "Love, and be silent" and “Unhappy that I am, I cannot heave / My heart into my mouth. I love your majesty / According to my bond; no more nor less,” Lear feels offended by Cordelia. He refuses to acknowledge his daughter and denies her inheritance. His anger toward her is strong:
By all the operation of the orbs
From whom we do exist and cease to be;
Here I disclaim all my paternal care,
Propinquity and property of blood,
And as a stranger to my heart and me
Hold thee from this for ever.
The intensity of Lear's language reflects how deeply Cordelia affected him. When he "disclaims" his paternal responsibilities toward her and deems her as a "stranger to my heart," it is clear Lear feels the bond between them cannot be restored. As a result, Cordelia does not really leave the kingdom. Rather, she is exiled, sent out by her father.