Let's start with the sentence that makes this whole topic easier to think about.
You are not uninsured. You are self-insured. Those are different things, and the difference is whether you know it.
Fewer than one in ten older Americans holds a long-term care insurance policy. The rest are covering the risk out of their own balance sheet, mostly without ever having made that decision on purpose.
So the real question is not "what happens if I have no insurance." It is "how does self-insuring actually work, and what is my backstop when the self-insurance runs out."
Both of those have concrete answers. Neither answer is "you are on your own."
Here is the whole map, in order of who pays first.