Haven't we already played this game?
After WWII the West and the Soviets split Germany. East Germany has socialism, where everyone's needs were provided for. West Germany had a capitalist system, where people got what they worked for. Well it didn't take long for people working in the East to figure out that they could do much better in the West, so they left. Yes, some of it was politics, yes some of it was about freedom. But the Berlin Wall wasn't built to stop political activists, pensioners, university students, or those in need of longterm care from fleeing. It was to stop professionals: engineers, technicians, physicians, teachers, lawyers and skilled workers. The drain of those with the largest net contribution to society was crippling the East German economy. So they built a wall to stop them. It's not an accident that most socialist countries enforce(d) exit visas.
Here in Canada we already enjoy a brain drain of our medical professionals. Why stay in Canada with lower incomes and higher taxes, when you can jump across the boarder and make out so much better. And I predict that Finland will see the same thing. Many Fins already speak Swedish and English so the barrier to exit is low. If you are a high paid professional why lose a huge chunk of your income to those who don't work when you can leave via the Schengen agreement.
Now might say that it won't cost extra because we will cut funding in other programs. Well that's bullshit. But don't take my word for it, or the media's word for it, sit down and do the math yourself. Basic income that provides any meaningful level of income is crazy expensive, well beyond what a few cuts here and there is going to cover.
You might say that only a few people care enough about higher taxes to leave. And you would be right. The problem is that it is the people who pay the most taxes who are going to leave. And when they leave the tax burden on those who stay goes up. Which creates more incentive for people to leave. It's a vicious cycle where the highest taxed leave and the next highest tax bare the burden.
I'll leave you with a thought experiment. Let say a nice liberal state like Vermont decided it's going to implement basic income, but no other state in the union follows suite. What do you think would happen?