Typical indicators of a failed state are usually described as  the ability to project power and  to protect borders and sovereignty, as in this definition in the Encyclopedia Britannica written by Naazneen H. Barma, Assistant Professor of National Security Affairs, Naval Postgraduate School, Monterey:
Failed state, a state that is unable to perform the two fundamental functions of the sovereign nation-state in the modern world system: it cannot project authority over its territory and peoples, and it cannot protect its national boundaries.
The governing capacity of a failed state is attenuated such that it is unable to fulfill the administrative and organizational tasks required to control people and resources and can provide only minimal public services. Its citizens no longer believe that their government is legitimate, and the state becomes illegitimate in the eyes of the international community.
In this regard, the U.S. is not [yet] a failed state. But Barma’s definition goes well beyond state violence, to state competence and the ability to provide for its citizens. In this regard, the U.S. is already a failed state:
Often, the executive barely functions, while the legislature, judiciary, bureaucracy, and armed forces have lost their capacity and professional independence. A failed state suffers from crumbling infrastructures, faltering utility supplies and educational and health facilities, and deteriorating basic human-development indicators, such as infant mortality and literacy rates. Failed states create an environment of flourishing corruption and negative growth rates, where honest economic activity cannot flourish.
The dynamics leading to and compounding state failure are many and varied, including civil war, ethnic violence or genocide, and predatory government and bureaucratic behavior. State failure comes in degrees and is often a function of both the collapse of state institutions and societal collapse. A strong state provides core guarantees to its citizens and others under its jurisdiction in the three interrelated realms of security, economics, and politics.
A failed state cannot maintain a monopoly on the legitimate use of violence and minimize internal conflict. It cannot formulate or implement public policies to effectively build infrastructure and deliver services or effective and equitable economic policies. In addition, it cannot provide for the representation and political empowerment of its citizens or protect civil liberties and fundamental human rights. Thus, state failure manifests itself when a state can no longer deliver physical security, a productive economic environment, and a stable political system for its people.