It is her love that keeps her hope for Lear. .
In spite of the fact that her heart and intentions are pure, Cordelia is finds herself unable to accomplish her goal. Her honesty gets her banished in the first scene of the play leaving her helpless to do anything to save her father, and leaving him in the hands of her undeserving sisters. Her desperate attempt, to appeal to them, goes unheeded. Cordelia was banished by her father, in spite of the fact that until this point she is his favorite; "now our joy, although the last, not least" (1.1.84). As a women, she has very little value, and as the third daughter, even less. She is the youngest, and her two older sisters are already married. Once married, a woman essentially becomes her husband, which is why Lear talks of giving the land to his son in laws and not his daughters. This makes Cordelia essentially expendable, she is unattached and therefore really has no value. The quality that is likely why Lear loved her most is also what prevented her from taking care of him. Her position as a single young woman, who is the third in line makes her less threatening, but also gives her character less persuasion. Her banishment puts on hold her plans to help save Lear. .
The fool has a very familial relationship with Lear, and a love similar to that of a child. He's almost like a sassy son to Lear. The language between the two, calling each other "boy, lad, and Numncle" indicates they have known each other for a very long time. Lear may have even known him since he was a boy. They are very familiar with each other, creating a unique but strong bond. This connection leaves the fool wanting to help, and Lear intrigued to listen. Although they are not related, the fool's motivation and drive was very similar to Cordelia's. He sticks with Lear through everything, a constant companion till his death. Lear is very stubborn and since he was once a king, he doesn't take direction well at all.
