Edgar Poe (it seems he disliked being called "Edgar Allan Poe") wrote a short story with the interesting title The Imp of the Perverse. The narrator is a murderer who seemingly commits a murder for which he cannot be suspected, but is compelled to admit the crime, thereby assuring his conviction and ultimate death by hanging. He's compelled to admit the crime not by interrogation or happenstance, but by his own urge to do so, despite knowing he need not and knowing that by doing so he's effectively killing himself.
It's a story that describes an irresistible self-destructive impulse, then. Of course, given Poe's personal history, many have suggested he was himself a victim of the Imp and that the story was a kind of confession. Unfortunately for Poe, the story was panned by the critics of the day, who evidently were unable to tolerate or even consider the thought that the Imp could exist.
Poe could be a rather savage critic himself. He was prone to dispute with his rivals, and was especially fierce in his quarrel with and condemnation of Longfellow. If you've ever read Longfellow, particularly his famous Song of Hiawatha, you know how annoying his poetry can be and like me may be inclined to sympathize with Poe. But you might also be unsurprised by the criticism Poe received and that he was upset by it.
The Imp should have been a recognized figure even then, however, as our self-destructive impulse has been apparent throughout recorded history. But perhaps the classical nature of education at that time inclined those who recognized it to ascribe it to hubris, the fate of those whose pride offended the gods, or in any case thought it to be a function of the just wrath of God, or the machinations of the Devil.
Since Poe wrote the story, though, we've become familiar with the Imp, who made appearances in the work of Dostoevsky and others, and of course in Freud. In fact, the Imp has even become a regular in various films, TV series and specials, not to mention its presence in courtrooms and the ubiquitous news media. The Imp is still portrayed as irresistible, and as overcoming the reason of heroes and villains alike.
I'm not so sure. Although there may well be circumstances where the urge to self-destruction is overwhelming and caused by genuine mental illness, I think the Imp must be indulged in order for it to destroy us.
As I'm an aspiring Stoic, I ask myself how the Imp would have been perceived by the ancient Stoic philosophers. The Stoics thought suicide to be an option available where it was not possible to live according to nature, but didn't deem it to be virtuous in itself. Self-destruction was not a goal of the sage except in limited circumstances. Otherwise, I think it would have been considered contrary to reason and to the Divine Reason (the creative aspect of the universe) in particular. It's in our nature to die, but not in most cases to cause our own death.
I think the Imp would have been considered perhaps the ultimate instance where emotions such as fear, guilt, and despair, which are in our control, were left uncontrolled. Succumbing to the Imp would be seen as something the Stoic Sage could not do.
The Imp, I would say, isn't something which is not in our control, to which we should be indifferent according to Stoic thought. It's not a disturbance resulting from our preoccupation with what others think and do, or from our desire for things in the control of others. It's rather a failure on our part to do the best we can with what's in our control, i.e. ourselves.