I had never heard of this case before; the way I read it, the southern states were never considered not part of the Union. (interesting)

Facts of the case

In 1851, Congress authorized the transfer of $10 million worth of United States bonds to the state of Texas. The Reconstruction government claimed that the bonds had been illegally sold by the Confederate state legislature during the American Civil War. When the Reconstruction government tried to reclaim the bonds, Texas filed suit directly in the United States Supreme Court, which retains original jurisdiction in certain cases in which a state is a party. 

Question

1. Was Texas eligible to seek redress in the Supreme Court?
2. Could Texas constitutionally reclaim the bonds?

Conclusion

In a 5-to-3 decision, the Court held that Texas did indeed have the right to bring suit. The Court held that Texas had remained a state, despite joining the Confederate States of America and its being under military rule at the time of the decision. The Court further held that individual states could not unilaterally secede from the Union and that the acts of the insurgent Texas legislature–even if ratified by a majority of Texans–were “absolutely null.” Even during the period of rebellion, however, the Court found that Texas continued to be a state.

White, 74 U.S. 700 (1868) States do not have the right to unilaterally secede from the United States, so the Confederate states during the Civil War always remained part of the nation.

And it was final. The union between Texas and the other States was as complete, as perpetual, and as indissoluble as the union between the original States. There was no place for reconsideration or revocation, except through revolution or through consent of the States.

The outcome: The Supreme Court ruled (5-3) that secession is constitutionally void, determined that Texas had remained a state throughout the civil war, and ruled that the state of Texas was entitled to the money Congress agreed to give it.

In Texas v. White (1869), the Supreme Court ruled unilateral secession unconstitutional, while commenting that revolution or consent of the states could lead to a successful secession