The thing that should be remembered (leaving Krugman aside here) is that we’ve usually two or more things going on at any one time, two things that are often working in opposite directions. The final result is the combined effect. We cannot thus start to insist that “x” is obviously, always and eternally true. The true answer in economics is almost always, well, it depends.
Does unemployment pay raise the unemployment rate?
As here, there’s some less unemployment as a result of the unemployed having some money and thus adding to aggregate demand. But we also get longer periods of unemployment and more of it as a result of people not being so desperate to get back into work before they starve. It’s the balance that matters.
And there’s an interesting test of what that balance is. The difference between EU and US long term unemployment rates. They, traditionally, only pay 26 weeks of unemployment benefit. We pay indefinately. We have rather higher long term unemployment than they do.