In an example of foreshadowing, O. Henry brings up the topic of ghosts on the first page of the story:
Hence the houses of this district, having had a thousand dwellers, should have a thousand tales to tell, mostly dull ones, no doubt; but it would be strange if there could not be found a ghost or two in the wake of all these vagrant guests.
When describing how “it would be strange if there could not be found a ghost or two in the wake of all these vagrant guests” in the furnished rooms on the Lower West Side of New York City, O. Henry foreshadows the big reveal that Eloise killed herself inside her furnished room and has become just such a ghost. Though she does not become a ghost that the young man can see, he can both smell and feel her in the room, even when he doesn’t know that she stayed there before.
That O. Henry uses the language of “a ghost or two” indicates that he may also be foreshadowing the young man’s death here as well. Readers do not see the young man become a ghost, but, in the wake of his suicide, it’s likely that he will haunt the room along with Eloise.