Foreshadowing, if used correctly, can deepen the understanding of a text by providing subtle clues as to its eventual direction or meaning. While the story "The Wife of his Youth" is not necessarily subtle in its foreshadowing, especially to the reader of today, it still uses narrative elements to set up the ending in a way that is not immediately obvious. For example, the name of Mr. Ryder's social group, "The Blue Veins," is used to demonstrate how social class was considered appropriate and desirable, even when the attainment of that social class causes one (as Ryder later acknowledges) to reject his past as "lesser."
Another good example is the mention of Ryder's age: "he was old enough to have been [Molly Dixon] father, though no one knew exactly how old he was." This sets up the eventual revelation that Ryder, although seemingly younger and in better health, is roughly the same age as Liza Jane, whose face "was crossed and recrossed with a hundred wrinkles."
One excellent example comes at the end of the first part of the story, where Ryder explains his views on people of mixed race.
"Our fate lies between absorption by the white race and extinction in the black. The one doesn't want us yet, but may take us in time. The other would welcome us, but it would be for us a backward step. 'With malice towards none, with charity for all,' we must do the best we can for ourselves and those who are to follow us."
(Chesnutt, "The Wife of his Youth," theatlantic.com)
Here it is clearly seen that Ryder considers "whiteness" to be a desirable forward goal, and "blackness" to be an undesirable backwards goal. While the black race may accept Ryder and people of mixed races, he sees that as a worse option than continuing to be "absorbed" by the white race. In other words, just as he has subsumed his own origins in order to be socially accepted, so to he believes that mixed-race peoples must strive towards "whiteness," rejecting "blackness" as a dead-end of the past. Of course, at the end, the exact same moral conscience that Ryder believes must reject "blackness" demands that he acknowledge, support, and praise his long-lost wife, even to the extent of threatening his own social status. Ryder sees, as does the reader, that skin color is truly a meaningless issue; the only moral obligation is how we treat our fellow human beings, whatever their past, present, or future.