You have actually used the word in your question: such tales are parables. The term parable often is given narrow application that refers to specifically a story from the Gospels that illustrates a specific moral teaching, such as the parable of the Good Samaritan.
But more broadly, the term is used in non-Biblical contexts too. For example, the stories of the 19th C Hindu teacher Ramakrishna Paramahamsa are also called parables, as can be seen at the website of a monastery of the order he founded. Here, in its entirety, is one of Ramakrishna's parables:
Once a man went to a certain place to see a theatrical performance, carrying a mat under his arm. Hearing that it would be some time before the performance began; he spread the mat on the floor and fell asleep. When he woke up all was over. Then he returned home with the mat under his arm!
Quoted by Mayank Bhatt in his blog, Generally About Books, entry for 28 February 2015. Accessed 4 January 2021.
Richard Eastman distinguishes between such brief, pointed narratives and more complex ones of the sort the question mentions (e.g., Carver). He says that Bible stories are closed parables. Discussing the Good Samaritan story, he says:
As itself—a parable, a brief and plausible allegory, a concrete analogue of a general ethical situation—Jesus' story stands single and unburied, a "closed" image.
When consistently expanded to include some complexity of incident, distinctness o characterization and fullness of setting, the closed parable becomes a story with its own narrative appeals. A list of examples would include Dickens' A Christmas Carol, George Eliot's Silas Marner, [etc.] ... In all, however, the ethical analogy which is the animating idea of the parable remains clearly distinguishable beneath a consistent narrative surface. (p. 17)
Eastman, Richard M. “The Open Parable: Demonstration and Definition.” College English, vol. 22, no. 1, 1960, pp. 15–18. JSTOR, www.jstor.org/stable/373858. Accessed 4 Jan. 2021.
Eastman contrasts closed parables with modern works by writers such as Kafka and Beckett, which he calls open parables:
a small genre of modern narrative brought to high intensity by such writers as Kafka and Beckett. Its difficulties arise from the misapplication of conventional reading attitudes, usually abetted by the logical refusal of its authors to explain "intention." (ibid.)
He says that in an open parable, the ethical point of the narrative is not straightforward, but needs to be worked out by the reader. Furthermore, different readers may reach different conclusions about what that ethical point is:
Like a kind of literary Rorschach blot, the open parable apparently puts it up to the reader to perform the creative act, to take his own direction so that he may find, in the general richness of theme, an ethical pattern which speaks most directly to him. This is the first pleasure of the genre. But the open parable is a controlled and controlling art-work, not a random blot. ... The attentive reader will discover that no one expression will prove out as the meaning. (p. 18)
James Champion argues for a similar definition of parable without making the distinction between open and closed parable:
the parable is unusual not because of its great variations in length, but because it is a form in which substance is warranted to break through form. Parabolic form in both ancient and modern cultures is determined by the reach of substance. (p. 35)
Champion, James. “The Parable as an Ancient and a Modern Form.” Literature and Theology, vol. 3, no. 1, 1989, pp. 16–39. JSTOR, www.jstor.org/stable/23926661. Accessed 4 Jan. 2021.
By substance Champion means the narrative elements that force existential and philosophical reflections on the reader's part.
The term parable is used not just by academic scholars, but also by creative writers themselves. John Patrick Shanley's best-known play is the Tony- and Pulitzer-winning Doubt: A Parable, which tells the story of a priest whom a nun accuses of molesting one of his (male) teenage charges. The ethical dilemma that the play presents is not clearly resolved, but the spectator is left to ponder upon the story and draw out lessons. The action is structured such that spectators will differ on exactly what the lesson is.
These works, however, have a complexity that seems somewhat antithetical to the sort of story the question focuses on. It seems that you're interested specifically in stories where the character ends badly and thereby serves as a cautionary symbol. I'm not sure Carver's tales are as clearcut as that in their moral. But if you believe they impart straightforward moral lessons about alcoholism, adultery, etc., you could adopt Eastman's term and call them closed parables. Or you could simply refer to them as object lessons, which Merriam-Webster defines as:
something that serves as a practical example of a principle or abstract idea.
Or you could use another term included in your question: cautionary tales. The Cambridge Dictionary provides a broad and simple definition:
a story that gives a warning:
Her story is a cautionary tale for women traveling alone.
Cautionary tales aren't restricted to folklore, nor to animal characters. On the contrary, stories like "The Fox and the Grapes" or "The Ant and the Grasshopper" are always called fables, rarely if ever cautionary tales. Cautionary tales typically involve human beings who come to unfortunate ends due to their own foolish actions.