King Lear and Cordelia's relationship is characterized by loyalty and betrayal. When Cordelia refuses to flatter her father and appease his vanity, Lear betrays his role and responsibilities as her father. He turns his back on her, with very cruel and hateful words, and sends Cordelia into exile. She is put not only out of her home, but out of her country. Despite all that Lear does to her, however, Cordelia remains loyal to him. She does not stop loving him, and she is the daughter who acts to save him after he is then so horribly betrayed by her sisters, Goneril and Regan. Because of her loyalty, Cordelia and her father are reunited, if briefly, and Lear comes to understand the selfless nature of his daughter's love for him. He seeks her forgiveness. Cordelia dies knowing that her father loves her, too, but Lear lives, mourning her loss and tortured by his role in her destruction. Very tragic indeed.
Cordelia's relationship to Lear is one great example of loyalty from the play. She is disowned, quite literally, by King Lear yet she urges her husband to help Lear when he is in need. She maintains the same filial loyalty throughout the play, regardless of adverse circumstance (while also refusing to embellish or exaggerate her affections).
There is a lot in Lear about the difference between words and actions. Goneril and Regan betray Lear, but Kent remains loyal to Lear. And yet in the beginning, Lear trusts Goneril and Regan a lot more than he listens to Kent.
Kent stays very loyal. How many people would disguise themselves and go back to serve someone who threatened to kill them? Really.