The below three quotes from Arthur Schopenhauer succinctly encapsulate both the essence of tragedy and the necessary compassion that the experience of tragedy in the theatre should engender. It is notable that tragedy should not lead to Aristotelian catharsis (the product perhaps of the second form of drama described in the first quotation below), but to a recognition of the profound suffering of each individual human being, and what ethic and morality to which that recognition should lead. They have relevance not only to the work of Samuel Beckett, but to the work of William Shakespeare, Sarah Kane and other tragedians as well.
Drama in general, as the most perfect reflection of human existence, has three modes of comprehending it. At the first and most frequently encountered stage it remains at what is merely interesting: we are involved with the characters because they pursue their own designs, which are similar to our own; … wit and humor season the whole. At the second stage, drama becomes sentimental: pity is aroused for the hero, and through him for ourselves. … At the highest and hardest stage, the tragic is aimed at: grievous suffering, the misery of existence, is brought before us, and the final outcome is here the vanity of all human striving. …[1]
At the moment of the tragic catastrophe, we become convinced more clearly than ever that life is a bad dream from which we have to awake. To this extent, the effect of tragedy … is the dawning of the knowledge that the world and life can afford us no true satisfaction, and are therefore not worth our attachment to them. In this the tragic spirit consists; accordingly it leads to resignation.[2]
The conviction that the world, and therefore humanity too, is something which really ought not to exist is in fact calculated to instil in us indulgence towards one another. … From this point of view one might indeed consider that the appropriate form of address between people ought not to be “monsieur,” “sir,” etc., but “Leidensgefährte,” “soci malorum,” “compagnon de misère,” “my fellow-sufferer.” However strange this may sound, it … reminds us of what are the most necessary of all things: tolerance, patience, forbearance and charity, which each of us needs and which each of us therefore owes.[3]
These quotations can be found in Gottfried Büttner’s essay “Schopenhauer’s Recommendations to Beckett,” which was published in Samuel Beckett Today: Endlessness in the Year 2000, pp. 114-122. The complete essay is downloadable here.
Footnotes

“I have presented such terrible images to knowledge that any ‘Epicurean delight’ is out of the question. Only Dionysian joy is sufficient: I have been the first to discover the tragic. The Greeks, thanks to their moralistic superficiality, misunderstood it. Even resignation is NOT a lesson of tragedy, but a misunderstanding of it! Yearning for nothingness is a DENIAL of tragic wisdom, its opposite!”–Nietzsche
With all due respect to Nietzsche, I find this strikes a hollow note. (Especially with all those exclamation points, which seems an attempt to convince himself.)
The Greek tragedians were moralists to greater and lesser degrees — certainly true of Aeschylus, but less so of Sophocles and Euripides. After the experience of Oedipus and Lear, of Beckett and Rothko and Feldman, I find in the embrace of Dionysian joy itself that same denial of, the same misunderstanding of, tragic wisdom. (And if Nietzsche can burden other commentators with the charge of error, so can he be burdened.) The tragic experience, for Schopenhauer (and for me), does not lead to cheer or joy.
Obviously Nietzsche repudiated Schopenhauer after The Birth of Tragedy, as is well known; but this is an accident of chronology, and I’m sure that Schopenhauer would have repudiated Nietzsche had the shoe been on the other foot.