The speaker of the poem actually appears to be a group of speakers. They are the Jews who are imprisoned in the concentration camp. They are almost like the members of a chain gang, singing a rhythmic song to pass the time, or just to stay sane. Some of the speakers are digging graves, while others are playing the "Deathfugue." They are all tired, worn out, and mostly without hope.
The cyclic nature of the fugue form and the disjointed nature of the language create a hallucinatory effect. The speakers are not in a "normal" state of mind. Nor do you get the sense that they believe they will make it out of the camp alive. Their attitude towards death is almost one of pitch-black humor. They often sound ironic in repeating lines like "there you won't lie too cramped," but the line between the irony and the literal is very thin in this poem.
The speakers are very attentive and they understand more than their jumbled syntax would suggest. They closely watch the movements of the guard, and they know about his literary pretensions. They see what the guard probably does not allow himself to see; that all his efforts to be cultured are undone by his barbaric actions during the day. The speakers themselves have a knowledge of German literature and music – maybe even an appreciation for it – which they find hard to reconcile with the situation that Nazism has placed them in.