What about Texans living in other states when independence happens?

They would not be cut off from home. A Texan who happens to be living in another state when independence arrives keeps their tie to Texas, and the path to Texas citizenship for people with a clear Texas connection is exactly the kind of detail the new nation would settle in its citizenship law. Independence is not a door that locks behind the people who are temporarily away.

A military posting or a job out of state does not erase being a Texan

Plenty of Texans are living elsewhere at any given moment: service members stationed at a base in another state, workers on a multi-year assignment, students finishing a degree, families caring for a relative. None of that makes them less Texan. A nation does not abandon its own people because they are temporarily across a line, and an independent Texas would have every reason to keep faith with Texans abroad, just as the United States keeps faith with Americans living overseas today.

Citizenship rules for Texans abroad are the new nation's to set, and the precedents are generous

Exactly how a Texan living out of state claims or confirms Texas citizenship is a question for the future Texas Legislature, the same as the rest of the citizenship framework. But the precedents all point one way. Nations routinely extend citizenship by descent and by prior residence, and they build straightforward processes for citizens abroad to register, vote, and come home. A Texan with deep ties to the state, family, property, a life built here, is precisely the kind of person a sensible citizenship law is written to include, not exclude.

Coming home stays open

There is no version of this where a Texan who was working in Denver or stationed in Virginia is barred from returning. Free people move toward home, and managed movement between an independent Texas and the United States is the easy part, handled the way contiguous neighbors handle it everywhere. We cover the travel mechanics in the answers on passports, freedom of movement, and the border with the United States. The point here is that the door home stays open.

Your US citizenship is unaffected

A Texan living in another state at independence remains a US citizen unless they choose otherwise, under the same settled law that protects every American from losing citizenship without clear intent. So a Texan abroad at the moment of independence is not forced to choose on the spot between Texas and the United States. The relationship between the two citizenships gets worked out in the transition, and dual status is the norm, not the exception. See the answer on keeping your US citizenship for the full picture.

The bottom line

Texans living out of state when independence comes keep their connection to Texas, keep their US citizenship, and keep a path home. The exact citizenship process for Texans abroad is for the future Texas Legislature to define, and every precedent favors including them.