When Popeye is jailed in the unnamed Alabama town for murder, "they" - presumably some combination of local policemen and the jailers - talk about how he'll send for his lawyer (310). It is also "they" who take Popeye to the place of his execution, and "adjust the rope" around his neck, "breaking his hair loose" (315).
Chapter 31 begins with Popeye being arrested (wrongly) "for the murder of a policeman in a small Alabama town" (302). Later, after he has been (wrongly) convicted for the crime, the novel provides one detail about the victim: according to Popeye's jailer, "folks here says that deppity invited killing" for the "two-three mean things folks knows about" (313).
The policeman from whom Popeye's grandmother asks for a match thinks her irrational statements (including the ominous "I bring down the house") are a deliberate effort at humor (307). He tells her three times that she "ought to be in vaudeville."
This is the neighbor of Popeye's mother who reports him for "cutting up a half-grown kitten" (309). It may be the neighbor who reported the fire in the boarding house earlier, but the text gives no indication of that.
After Popeye's grandmother leaves him on the seat of a parked limousine, the woman who owns the car becomes a kind of godmother to the child, making sure Popeye gets medical attention and often bringing him "to her home in afternoons and for holidays" (308). The narrative does not explain her motives in trying to help, but does show how they come to grief when her attempt to give him a birthday party is defeated by his violent antisocial behavior. Even after Popeye is sent to "a home for incorrigible children" (309), this woman continues to help Popeye's mother support herself (309).
This boy falls while delivering groceries to Popeye's mother on his bike. By breaking the bottle of olive oil she ordered, he sets off a series of unfortunate incidents - but is himself unapologetic about the original mishap, telling the customer "you ought to buy that oil in cans" and "you want to have that gate fixed" (305).
The Florida doctor whom Popeye's mother consults about her sickly child tells her to "feed him eggs cooked in olive oil" (305). (It is possible that Faulkner is making a strange and subversive reference to the cartoon characters Popeye and Olive Oyl; both these E. C. Segar characters had appeared in newspapers at least two years before Sanctuary was published.)
When Popeye's mother gets sick after her husband abandons her, it is "an old negro woman" rather than a doctor that she goes to, and the woman "tells her what was wrong" (304). The narrator doesn't tell us, but the problem is probably syphilis.