After the Madurai Sultanate assumed control over most of Pandya Nadu, and which was later captured by Vijayanagara Empire, the Southern Pandyas formed a rump state from 1330 to 1422 ruling over modern day Tirunelveli and Thuthukudi districts along with certain regions of Western Ghats. They further lost their territory and ruled from Tenkasi region as Tenkasi Pandyas formed a rump state there until 1623.
The Hungarian Soviet Republic was proclaimed in March 1919 after the resignation of the government of the First Hungarian Republic when, following their absorption of the Social Democrats, the Communists took control of the country. Though sometimes controlling only around 23% of the territory of the Hungarian state, after some initial military successes, in the end the army was defeated and the government fell in August 1919.
In the manga and anime series Attack on Titan, the nation of Eldia existed in an upside down map of Africa. It later grew unstable due to internal conflicts between the families with the power of the Titans, and collapsed during the Great Titan War a century ago. Eldia lost most of its land as well as seven of the Nine Titans to a newly reborn Marley, a nation long persecuted by Eldia, and many Eldians retreated to Paradis Island, the surviving rump state of Eldia. The 145th Eldian King, Karl Fritz raised the Walls with thousands of Colossal Titans to protect Eldia from Marley and the other nations of the world, and erased the memories of Eldia from the ethnic group, the Subjects of Ymir inside. In Marley, the remaining Eldians of the mainland would then be forced into internment zones, where they would be treated as second class citizens and later became a colonial empire.
^Krasner, Stephen D. (2001). Problematic Sovereignty: Contested Rules and Political Possibilities. Columbia University Press. p. 148. For some time the Truman administration had been hoping to distance itself from the rump state on Taiwan and to establish at least a minimal relationship with the newly founded PRC.
^ abTir, Jaroslav (2005). "Keeping the Peace after Secession: Territorial Conflicts between Rump and Secessionist States". The Journal of Conflict Resolution. 49 (5): 714. doi:10.1177/0022002705279426.