Endgame's opening lines repeat the word "finished," and the rest of the play hammers away at the idea that beginnings and endings are intertwined, that existence is cyclical. Whether it is the story about the tailor, which juxtaposes its conceit of creation with never-ending delays, Hamm and Clov's killing the flea from which humanity may be reborn, or the numerous references to Christ, whose death gave birth to a new religion, death-related endings in the play are one and the same with beginnings. While Hamm and Clov are in the "endgame" of their ancient lives, with death lurking around the corner, they are also stuck in a perpetual loop that never allows final closure—Hamm claims he wants to be "finished," but admits that he "hesitate[s]" to do so. Just as death cannot arrive to seal off life, neither can Hamm or Clov escape to close the book on one existence and open another—note Clov's frequent failed attempts to leave the room (and his final return after vowing to leave) and Hamm's insistence on returning to the center of the room. Nell's death may be an aberration in a play where death seems impossible, but since she is the one character who recognizes the absurdity of the situation, perhaps she is rewarded by dying.
Several of Beckett's dramatic designs elucidate this notion of a circular existence. As mentioned above, Hamm has a compulsive need to return to the exact center of the room after Clov takes him on chair-rides. His oblique comments about the environment—beyond the hollow wall in their hole is the "other hell"—suggest an allusion to Dante's Inferno, another work that used images of circularity. And just as Dante's infernal images emphasize the eternal misery of its inhabitants, Beckett's characters are stuck in eternally static routines. They go through the "farce" of routine actions, as they call it, because there is nothing else to do while they wait for death. Even the environment around them is static; everything outside is "zero," as Clov reports, and the light, too, is forever gray, stranded between light and dark.
Beckett also makes use of repetitions to underscore the cyclical stasis in Endgame. The play systematically repeats minute movements, from how many knocks Hamm makes on a wall and how many Nagg makes on Nell's ashbin to how many steps Clov takes. The repetitions prohibit the discernment of meaning, since there is never a final product to scrutinize. At the start of the play, Clov questions when individual grains become a "heap." In his view, the heap is "impossible"; any single grain is not a heap, and a "heap" is just an accumulation of single grains. When Hamm later considers how individual moments make up a life, the analogy should hold—it is an "impossible" life, consisting not of a life but of discrete moments, until death terminates it. At one point, Hamm excitedly believes he is "beginning" to make some meaning out of the environment, but he will keep beginning to make sense of it and never finalize the meaning.
The constant tension in Endgame is whether Clov will leave Hamm or not. He threatens to and does sometimes, but he is never able to make a clean break. Likewise, Hamm continually tells Clov to leave him alone but pulls him back before an exit is possible. Both wonder out loud why they stay with each other, but both men give reasons in long monologues for why they put up with each other: their empty lives are filled only with unyielding pain, and none of life's typical consolations help them—there is no cure for being on earth, as Hamm often says. One of the unspoken themes in the play is that having someone else around, even an irritant, helps assuage that pain. But Hamm and Clov's unwillingness to face this pain alone somehow makes the pain greater, and their complementary, dominant-submissive pairing (a staple of Beckett's plays) highlights their numbing dependency. Beckett has compared Hamm and Clov's tense co-dependency to his own relationship with his wife in the 1950s; both wanted to leave the other, but were afraid to. Nagg and Nell have a happier marriage in part because Nell, at least, is willing to accept that they cannot rely on each other (she calls their futile kissing routine a "farce") and must exist in their separate ashbins.
Beckett was one of the lynchpins behind the French theatrical movement called the Theatre of the Absurd. The Absurdists took a page from Existentialist philosophy, believing that life was absurd, beyond human rationality, meaningless, a sentiment to which Endgame subscribes, with its conception of circularity and non-meaning. Beckett's own brand of Absurdism melds tragedy and comedy in new ways; Winnie gives a good definition of his tragicomedy when she says, "Nothing is funnier than unhappiness" (Beckett believes this was the most important line of the play). Self-conscious form in the theater was another feature of Absurdism, and there's no shortage in Endgame, from Clov's turning the telescope on the audience to Hamm's showy references to his own acting. But Beckett's self-consciousness is not merely for laughs. Just as the characters cannot escape the room or themselves, trapped in self-conscious cages, neither can the audience escape their lives for a night of theatrical diversion.