Would there be a transition agreement so benefits don't just stop?

Yes. Benefits do not stop the morning after a vote, because a vote is the start of a negotiated process, not a switch that flips. Continuity is the entire design, and both governments have every practical reason to preserve it.

A vote opens negotiation, it does not end anything

The single most common misunderstanding about independence is that it happens in one dramatic instant. It does not. A referendum is the starting gun. What follows is a negotiated transition, conducted the way every modern separation has been conducted, in which existing arrangements continue while the details are worked out. Benefits keep being paid during that period. There is no day when Texans wake up to find checks canceled and clinics closed, because that is not how any of this works.

The tools to keep benefits flowing already exist

Nations do not improvise this. The instruments that keep benefits moving across a border are standard and already in use. The United States maintains totalization agreements with more than two dozen countries precisely to keep Social Security, disability, and survivors benefits flowing to people who have lived or worked on both sides of a line. Tax treaties prevent double taxation. These are the ordinary furniture of relations between countries, and an independent Texas would use the same furniture. The mechanism is not theoretical. It is what lets a retiree in Lisbon draw her American Social Security right now.

Most of the machinery never leaves Texas anyway

Continuity is easier than people fear because so much of the delivery is already Texan. Medicaid, SNAP, unemployment insurance, and the hospitals and clinics that provide care are administered and operated in Texas today. The Texas Health and Human Services Commission, the Texas Workforce Commission, and Texas providers keep doing what they already do. For the earned federal benefits that are paid from Washington, like Social Security and military pensions, the payment systems already reach across borders. There is far less to "hand off" than the scare stories imply.

Both sides want the smooth version

Look at the incentives. A chaotic separation that interrupted benefits would be a disaster for Washington too. The United States collects taxes from citizens abroad, including from working Texans, and it has no interest in the legal exposure, the international embarrassment, or the economic disruption of cutting off benefits to millions of people who earned them. The cheaper, calmer, mutually beneficial path is a negotiated transition that keeps payments running. That is the path nations almost always choose, because the alternative serves no one.

Texas plans for the bad-faith case too

Responsible planning does not assume good faith and hope. If Washington ever refused to honor what it owes Texans who paid in, Texas holds the strongest card at the table: the roughly $7.7 trillion in Social Security and Medicare benefits Washington owes Texans, which can be netted against any debt share. And on the programs Texas already runs and funds, Texas simply keeps running and funding them. The floor under every vulnerable Texan is that Texas takes care of its own, with the means to do it.

The bottom line

There is a transition agreement by design, benefits keep flowing through it, the cross-border tools already exist, most of the delivery never leaves Texas, and both governments have every reason to keep it smooth. Nobody's check stops on day one.