A state, in the Weberian definition, is the entity that successfully claims a monopoly on the legitimate use of violence within a given territory. A failed state is one that has lost this monopoly.
The dissolution here is not of borders but of authority. The government may still exist on paper — it may have a seat at the United Nations, a flag, a national anthem — but it cannot collect taxes, enforce laws, or control its territory. Somalia after 1991 is the canonical example: the central government collapsed, and power devolved to clans, warlords, and Islamist courts. The state dissolved into its pre-state components.
Failed states are not anarchic in the sense of having no order. They are anarchic in the sense of having too many orders, none of which can claim legitimacy over the whole. They are states that have dissolved from the inside out.
The term itself is contested. Scholars prefer "fragile state" or "state in crisis." But "failed" captures something essential: the state was supposed to work, and it did not. The dissolution of a state, like the dissolution of a marriage, is a failure of a particular kind of promise.
In Fiction
Robert Kaplan's The Coming Anarchy (1994) popularized the image of the failed state as a zone of chaos — West Africa as a Hobbesian nightmare of child soldiers and resource wars. The book was criticized as reductive but captured something real: the dissolution of state authority is never clean, never complete, and never without human cost.