The one exception to admitting incriminating statements in a trial that were made without administration of the Miranda warning is called the .

Public safety exception

Explanation:

The Miranda warning gives an individual protection in custody and protect from direct questioning which can result to compelled self-incrimination. The Miranda warning gives a suspect right to provide answers to questions from law enforcement.

However, there is a public safety exception, where suspect or defendant is required  to provide relevant information to the police at time needed, when it has to do with the safety of the public. This allows for statements to be used as direct evidence in the court.

The public safety exception is mostly applied when has to with cases involving dangerous weapons and  items which can be a public safety concern.