The truth that Cordelia tells Lear about the depth of her love is only rewarded by being disowned and losing all the wealth and land that she stood to gain had she, like her sisters, exaggerated her affections and lied about her love for her father. As a result, Lear is very open with Burgundy and France, the two monarchs who have come to try and marry Cordelia. He tells them that they can have her but that she will not receive anything from him. Burgundy, respectfully, says that on these terms he cannot marry Cordelia. Note what France says, however:
Fairest Cordelia, that art most rich being poor,Most choice forsaken, and most loved despised!Thee and thy virtues here I seize upon,Be it lawful I take up what’s cast away.