In the United States in the 19th century, upon the secession of Virginia from the union on April 27, 1861, anti-secessionist legislators convened a rump legislature and formed a pro-Union reformed government which claimed to represent all of Virginia.
This reformed government authorized the creation of the state of Kanawha, later renamed West Virginia.
By contrast, the Legislative Yuan of Taiwan between 1951 and 1991, having been relocated from Nanking to Taipei when the Republic of China lost its Chinese mainland in late 1949, contained members originally elected from mainland constituencies who could not be replaced.
The pre-reform Legislative Yuan was nevertheless widely regarded as a rump legislature, controlling only a fraction of the territory it claimed to represent.
Members died or defected to the Oireachtas of the Irish Free State until, in 1938, the remaining seven yielded their notional authority to the IRA Army Council.