How would that be accomplished? Do you hold a referendum and find out how many want independence and how many don't? What would be the cut-off - would it be a simple majority or a super majority? What if it was regionalized, for example if east Texas voted overwhelmingly to stay but west Texas voted overwhelmingly to go. Would you split the state and leave with only the western part? And what about the federal property in the state, the national debt, social security and medicare, how do you settle those?
I would suspect, though, secession would occur by a resolution passed by both houses of the legislature. You might very well have Virginia situations where parts of the state peel off, but these are questions that can't be answered until they happen. There's no precedent for this type of stuff.