The term debellatio or "debellation" (Latin 'defeating, or the act of conquering or subduing', literally, 'warring (the enemy) down', from Latin bellum 'war') describes a situation in which an interstate war ends not with a peace treaty nor a ceasefire, but with the catastrophic state collapse of the losing party as a result of comprehensive military defeat, typically resulting in the disintegration of the institutions capable of issuing an authoritative instrument of surrender.

Israeli law professor Eyal Benvenisti defines debellatio as "a situation in which a party to a conflict has been totally defeated in war, its national institutions have disintegrated, and none of its allies continue to challenge the enemy militarily on its behalf."

In some cases debellation ends with a complete dissolution and annexation of the defeated state into the victor's national territory, as happened at the end of the Third Punic War with the defeat of Carthage by Rome in the 2nd century BC.

The American Civil War did not end with the issuance of a formal instrument of surrender by the Confederate States. By April 1865, the Union had occupied most of the Confederacy's national territory, including its capital, all major ports, and most of its industrial capacity. Moreover, a comprehensive Union blockade had effectively cut off the Confederacy's access to foreign trade. Militarily, the Confederate States Army was disintegrating. The Confederate States Congress ceased to function on 18 March, seven days before the fall of the capital, adjourning sine die with the last entry in its official journal being "the Confederate Congress, with its work still undone went silent forever". The Confederate cabinet continued to meet to manage the increasingly desperate war effort but was unable to stave off collapse. On 9 April, following the Appomattox campaign, Robert E. Lee surrendered the main remaining Confederate force, the Army of Northern Virginia, at Appomattox Court House.

Despite the evident futility, Confederate President Jefferson Davis continued to attempt military resistance with such forces as remained under the control of the rapidly-disintegrating Confederate government, principally the Trans-Mississippi Department; Davis intended to cross the Mississippi and make a last stand. He attempted to organize a new army but was told this was impossible. Having failed to raise any new forces, and with the surrender of the Army of Tennessee and other forces under Joseph E. Johnston on 26 April depriving what remained of the Confederate government of some 100,000 additional troops, Davis accepted the inevitable. On May 5, he convoked the Confederate cabinet, such as it remained, in Washington, Georgia, and issued a proclamation declaring the dissolution of the Confederate States. On 9 May, Union President Andrew Johnson declared that the rights of the Confederacy as a belligerent power had come to an end. After 9 May, anyone fighting in the name of the now-nonexistent Confederacy was considered not a legitimate soldier but a bandit; as Ulysses S. Grant's General Order 90 put it, "any and all persons found in arms against the United States, or who may commit acts of hostility against it ... will be regarded as guerrillas and punished with death."

Nonetheless, military resistance by the remnants of the Confederate army continued for some weeks. The last substantial engagement of the war, the Battle of Palmito Ranch, was fought on 12–13 May in Texas, and the Trans-Mississippi Department under Kirby Smith, the last major Confederate force under arms, did not surrender until 26 May. On the same day, the Camp Napoleon Council of the Confederacy's indigenous allies was held to appoint representatives to negotiate the surrender of their forces; the last of these, under Stand Watie, stood down on 23 June. The last Confederate unit to surrender was the commerce raider CSS Shenandoah, which did not learn of the surrender until 27 June, and surrendered to the British government at Rock Ferry on 6 November.

The Confederate government never issued any formal capitulation or other instrument of surrender. By the time that President Davis accepted that defeat was inevitable, the Confederate capital had been taken and the government had effectively disintegrated, with the armed forces not far behind. Joseph E. Johnston stated of the situation at the time that "[w]ith such odds against us, without the means of procuring ammunition or repairing arms, without money or credit to provide food, it was impossible to continue the war except as robbers." The proclamation of 5 May dissolving the Confederacy simply acknowledged the situation as it was; by then, there had been no functional government for some weeks (at least since the fall of Richmond); the cabinet, such as it was, managed only a rapidly shrinking group of armies.

From a legal perspective, the victorious Union considered the entire existence of the Confederacy illegal; the absence of a formal instrument of surrender from a government that did not legally exist was irrelevant. Nonetheless, on 9 May, President Andrew Johnson formally extinguished the rights of the Confederacy as a belligerent power. The war legally came to an end on 20 August 1866, though there had been no fighting for more than a year by that point.