Although we are not told directly what happened at the end of the story, it is possible to infer why the knocking stopped and when the door was opened nobody was there to greet Mrs. White. Note how the last sentence of the penultimate paragraph tells us that:
He heard the creaking of the bolt as it came slowly back, and at the same moment he found the monkey's paw, and frantically breathed his third and last wish.
Mr. White, having understood the cadaver-like state that his son will be in, half dead and half alive, has recognised and understood the horror he is unleashing on the world and how it will destroy and upset his wife, who still thinks that the wish will somehow gain her back her son as she knew him. Thus, he manages to grasp the paw at the same time as his wife opens the door, and uses the final wish to send his son back to the grave - where he now belongs.
The fitting ending given to the story "The Monkey's Paw", has its own sinister appeal. The father understood about the devastating effects of the monkey's paw, or rather, the outcome of his own greed.
When Mrs. White wanted her son to return back she forced her husband to wish for the second time. After sometime, they hear knocking at the door. Mr.White fears the paw might come up with something fatal again, as it did to their son earlier. Hence, ----
He found the monkey's paw, and frantically breathed his third and last wish.
After that he found that there was no one at the door, and I am sure, he must have heaved a sigh of relief.