In terms of plot, "Black Sheep Astray" is the last in a sequence of near-future stories set in North Africa, which also includes Black Man's Burden (1961-2), Border, Breed nor Birth (1962), and The Best Ye Breed (1978).
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These stories, dated 1982-1986, are, like in the volume #1 Music for Mechanics, still science-fiction oriented, with monsters and extra-terrestrials.
They're given hope for a better life when a mining company shows interest in purchasing their homestead, but things become tense when Martha's brother Wade (Barlow Jacobs), who defected to the Union Army returns home after hearing of their father's death- unaware that Martha herself was the one who brought about his demise.
The title is a pun on The Black Man's Burden, an expression which refers to black slavery, used as the title of a book by E. D. Morel (1920) in response to the poem, "The White Man's Burden" (1899) by Rudyard Kipling, which refers to (and champions) American imperialism (including its history of slavery).
Elam, who recognized the bandit’s Griswold pistol, tells Durant (Colm Meaney) of the coincidence that the payroll arrives the same day the strangers do, as well as two Rebels buying a black man a drink.
The poem was originally written for Queen Victoria's Diamond Jubilee, but exchanged for "Recessional"; Kipling changed the text of "Burden" to reflect the subject of American colonization of the Philippines, recently won from Spain in the Spanish-American War.
The song describes a black man dealing with the oppression of a white boss, and considering a possibly violent reaction.