In terms of Edgar Allan Poe's "The Tell-Tale Heart," there are two possibilities to consider if the social aspect is changed.
The less significant aspect is the neighbors. It is they who, hearing the scream of the old man, summon the police. Had it not been for them, we can assume the narrator might get away with the deed.
That the narrator is mad is clear from the start:
TRUE!—NERVOUS—VERY, very dreadfully nervous I had been and am; but why will you say that I am mad? The disease had sharpened my senses—not destroyed—not dulled them. Above all was the sense of hearing acute... How, then, am I mad? Hearken! and observe how healthily—how calmly I can tell you the whole story.
It is ironic that hearing is what brings about the discovery of his deed: the neighbors have heard the noise from the house. However, it is also sound that drives the narrator to admit to the police what he has done because he "hears" the dead man's heart still beating.
(This sound may be the results of his madness, or he may actually have heard something and thought it the heart. Poe writes that the old man comes awake when the narrator's finger slips off the catch of the lantern—he may have remained awake because he heard bugs in the wall—he was...
...hearkening to the death watches in the wall.
This may also be what the narrator hears when the police come to investigate.)
Had the neighbors said nothing, the story would have been changed in that the narrator would have been left alone in his madness; but we can infer that the story would not have lasted long beyond the old man's death, for the heartbeat the narrator "hears" would probably have driven him to kill himself. As it is, he cannot wait for the police to leave before screaming out the truth because he cannot bear to hear what he believes to be the heart still beating.
The other aspect of society in the story is that of the old man and the narrator. They seem to be alone: with a housekeeper or perhaps a daughter of the old man present, there would have been others to step in on the old man's behalf. Even without knowing the narrator's murderous intent or his dangerous mental state, they could have reassured the old man and created (with their presence) an obstacle that might have kept the younger man away from the elderly one.
It would seem that the narrator has too much easy access to the old man. Had he been more distanced, the narrator might not have had the opportunity to develop his obsession with the old man's eye:
I loved the old man. He had never wronged me. He had never given me insult. For his gold I had no desire. I think it was his eye! yes, it was this! He had the eye of a vulture—a pale blue eye, with a film over it.
The old man's isolation makes him a perfect mark for the narrator's madness. The narrator reports that he watches the old man every night, stealthily easing his way into the room around the same time. It is obvious that he has free rein of the house and the old man when he reports visiting the frail homeowner early each morning:
And every morning, when the day broke, I went boldly into the chamber, and spoke courageously to him, calling him by name in a hearty tone, and inquiring how he has passed the night.
There is no one there to prevent the murder, only those to report sounds afterward: it is the absence of society that allows the death of the old man; but the neighbors' presence (and hearing) that exposes the murderer to the scrutiny of the police.