There are a few things that distinguish the character Nell from everyone else in Endgame. For one, she's the only character who dies. Now, think back to the one scene she has where she talks with Nagg. After reading this scene, if we had to guess which character was going to die, we'd probably have said Nell. The reason is that Nell is the character that seems to have given to despair.
She laughs once, when she and Nagg remember falling off their tandem bicycle and losing their shanks. But, she is the only character never to make a joke or a protest. There is a lot in her behavior that suggests that she has given up. If we stick with the metaphor of the endgame in chess, this might mean that she is the most experienced player – she has recognized that the game is over and is willing to just let it end.
Now, Nell's despair is tied in with another personal feature; she is the nicest character in the play. When Nagg hears Hamm complaining of something dripping in his head and wondering if it is his heart, he laughs. Nell, by contrast, says, "One mustn't laugh at those things, Nagg. Why must you always laugh at them?" (1.192) She still seems to have some sympathy for her son, and she tries to indulge Nagg as much as she can. This might suggest that her inability to be cruel is linked to her despair. The other characters manage to keep themselves from totally giving up hope by being cruel to each other. Since Nell has forfeited this capacity, she is the first to go.
Now, Nell may be the most minor character in the play, but she gets the best lines:
"Nothing is funnier than unhappiness, I grant you that… Yes, yes, it's the most comical thing in the world. And we laugh, we laugh, with a will, in the beginning. But it's always the same thing. Yes, it's like the funny story we have heard too often, we still find it funny, but we don't laugh any more." (1.194–196)
Nell has kept her sympathy, but she has lost her ability to laugh, a surefire mark of doom in a Beckett play, since Beckett often links laughter with survival in his work.
There is a last bizarre point, but we don't know what to make of it. Still, we'll throw it out there: Nell seems to be more concerned with accuracy then anyone else in the play. This comes up first when Nagg asks if Hamm has changed her sawdust, and she points out that it is sand. She asks, "Can you not be a little accurate, Nagg?" (1.178) We just bring this up because it is a feature that is peculiar to Nell.
We suppose that her longing for accuracy may fit in with her general gloominess – she focuses on the particular details of their awful situation. The flipside, however, is that she is the one who remembers most of the details from being on Lake Como. Both in happiness and sadness then, she clings to these particulars. If you think on it long enough, there could be more to it (as with almost everything else in the play).