When a drug addict is left a physical and mental wreck from their addiction to drugs or alcohol. The signs are typically what they would be in real life; their visage noticeably deteriorates, they are increasingly unreliable and regularly fail to meet obligations, are often visibly drunk or strung out and, if they are on drugs, may be associating with sketchy and often dangerous people, and are also prone to theft, scams, and scheming to acquire money to feed their habits. The decline is often documented as a way of showing Drugs Are Bad and may be the focus of a Very Special Episode. This is distinct from the Functional Addict (who is still capable of accomplishing the tasks of everyday life), but the Functional Addict may reach this state. In cynical works, this can be the endpoint of a Descent into Addiction character arc.
Also distinct from The Alcoholic (where the character trait is simply that they are usually drunk), but there definitely can be overlap.
The Logical Extreme is someone being killed by their addiction, often a Long-Lost Uncle Aesop so that none of the main cast needs to die. If they get support and have great Heroic Willpower, they may become a Recovered Addict. Goes with Fiending for a Fix, where addicts become dangerous or unscrupulous because they're acting on cravings or suffering from withdrawal.