Virginia v. West Virginia (78 U.S. 39 (1871)) was an 1871 case before the Supreme Court dealing with the establishment and boundaries of West Virginia. Although the case was not explicitly about the secession of West Virginia, it tacitly dealt with the constitutional issue of how new states can be created.
At the start of the Civil War, Virginia was divided. The eastern, agricultural counties of the state, dependent on slavery, considered themselves part of the south. The mountainous counties of the west were more closely related to the rest of the union, and when Virginia decided to join the rest of the south, the western counties broke off, forming what was at first a loyalist government of Virginia, and which then became a separate state. At the time this happened, as battles were raging across the area, the exact legal status of the entity was perhaps not at the top of people's minds. As well, because the area was in the middle of a war, the political and legal status of the area was established more as a matter of military control than of popular sovereignty. After the war was over and reconstruction was going on, the issue came to court, especially in regards to the exact boundaries of Virginia and West Virginia, since it couldn't be claimed that all areas had declared their political allegiance free of duress.
There is also a section of the United States Constitution that states:
(Article IV, Section 3)
New states may be admitted by the Congress into this union; but no new states shall be formed or erected within the jurisdiction of any other state; nor any state be formed by the junction of two or more states, or parts of states, without the consent of the legislatures of the states concerned as well as of the Congress.
What this means is that the United States can not partition or fragment states without the states allowing it to happen. During the war, the separation was necessary, but after the war, wouldn't the state of Virginia be allowed to reabsorb the territory, or at the very least say what its boundaries would be?
The Supreme Court decided that West Virginia was created with the consent of the legislature of Virginia. At the time, this was the "Reorganized State of Virginia", meaning the Union government that existed in the area that is now West Virginia. That entity, considered to be the legal representative of all of Virginia, declared that West Virginia could form its own state. The Supreme Court found that while the federal government needed consent of a state's legislature to enact a partition, the federal government also could decide what the state's legitimate legislature was.
Theoretically, this means that the federal government could designate any arbitrary group of people to be a state's "legitimate government" and use their permission as the legal requirement to partition a state. Could the United States President and Congress designate the patrons of a Marin County coffee shop to be the legislature of California, and get them to say "okay" to a separation of California? Theoretically, this ruling does allow that.
However, this ruling, which deals with the last time that one of the United States was separated in two (the previous instance being the creation of Maine out of Massachusetts as part of the Missouri Compromise of 1820), came about because of a unique circumstance in United States history. Outside of the context of The Civil War, a conflict that tore the United States apart, rewrote the political and geographic map, and exhausted the nation, the Federal Government's decision to allow a seemingly arbitrary legislature to pronounce itself the legitimate legislature seems odd. However, at the time, when the nation was on the brink of collapse and there was, to say the least, a less than sympathetic attitude towards the "real" government of Virginia, the ignoring of the legal niceties of Article IV makes a lot more sense. In other words, no matter what theoretical application could be made of Virginia v. West Virginia, it would only become a practical issue in a situation where we had much more pressing things on our minds.
The text of the 1871 case, which can be hard to read due to both 19th century stylistics and legalese, can be found here: