In Property, Walter is the son of Sarah, the narrator Manon's "house slave," and of Manon's husband, the plantation owner.
The backstory of this is that Manon first becomes aware of her husband's "activities" after he finds out that Sarah intends to marry Bam, his butler. Manon's husband flies into a rage and has Bam beaten to a pulp. Soon Sarah is pregnant with Walter by the "master," Manon's husband.
The secret history of slavery was "miscegenation," occurring as it did in the white masters forcing themselves upon their female slaves. In Property, the child Walter appears suddenly in front of a dinner guest, to whom his resemblance to Manon's husband is more than obvious. Walter has rushed wildly into the dining room, "gibbering" and throwing himself upon the guest, Mr. Borden, who meaningfully asks, "What have we here?" To Manon Walter is a "mad creature," undisciplined and, in this first appearance, animal-like. The moment is hugely embarrassing because the multi-racial child is obviously the son of the "owner."
The wildness of Walter is in fact about as clearly metaphorical as one could imagine of the dysfunctional and criminal nature of the slavery system. He is evidence, in a way humiliating to the master's wife, of the power dynamic at the heart of this system, in which the slaveowners use their "property" for sex. What makes this aspect of the system especially egregious, of course, is the hypocrisy by which "miscegenation" was publicly regarded the worst possible thing, because the mixing of races implied the obliteration of the whites as a race. Yet it was the activity that the practitioners themselves engaged in.