how does the author use foreshadowing to contribute to the story’s overall meaning?

The Sergeant Major pretty much tells the White family the fate of others who have used the paw:

"The first man had his three wishes. Yes," was the reply; "I don't know what the first two were, but the third was for death. That's how I got the paw." "If you don't want it, Morris," said the other, "give it to me." "I won't," said his friend, doggedly. "I threw it on the fire. If you keep it, don't blame me for what happens. Pitch it on the fire again like a sensible man."

Another example of foreshadowing is the bad weather at the beginning of the story foreshadowing evil that is to come. There are hints that this paw is ominous and destructive all the way through the story.