The withdrawal of a state from the union is called

Secession is when a state decides to withdraw from the Union.

The act of withdrawing a state from the Union of the United States is called "secession". By definition secession has happened in many countries throughout the years, but the most relevant example of secession in the United States occurred in the 1860s with the secession of 11 states from the United States who formed their own government and declared themselves the "Confederate States of America". What resulted was the Civil War, which lasted from 1861 until 1865 when the Confederate States of America were defeated and forcibly re-entered into the United States.