If a minority of voters are dependent on the UBI and a majority decides that they do not like the system, or a politician persuades them so, they will vote against it. ("Working your ass off on lazy strangers" is a huge boon for populist politicians.)
If a majority of voters depends on the UBI and a minority is compelled to provide it to them, they basically have no recourse but to emigrate. At which point you lose their tax money, unless you impose draconic measures on emigration.
Which nation is that?
Otherwise, I can simply point out that many almost all the countries with single-payer health care are still plenty enough peopled to be able to pay for it and don't have to have any draconian policies against leaving. As I understand it, even residing outside of them often exempts you completely from taxation, which even the 'can't afford single-payer!' US doesn't do.