Amazing how often people seem to think this would be a net "money sink" by definition. Compare the following situations:
Person A is unemployed, and receives, say € 700 as benefits.
Person B has a job, and makes € 2000 per month. Versus
Person A is unemployed, but gets a basic income of € 700.
Person B gets a basic income of € 700, and has a job to earn an additional € 1300 a month.
It's simply a matter of choosing the numbers appropriately, and adjusting tax levels (and -perhaps- hourly wages etc) as necessary to compensate. Oh wait, that's not counting the large # of government bureaucrats who aren't needed anymore because the rules are simplified. So those bureaucrats can go do something that's more productive than count beans and meddle in other people's private affairs.
In short: there is money to pay for this, period. If only the political will exists. Especially in modern, wealthy western countries.
Personally I'm a big believer in this. For one, it could help greatly to equalize the power balance between employers and employees. In a largely capitalist society, that balance is skewed strongly towards employers. Employees are like water in the ocean, so employers can pick & chose at will. In theory employees can do the same. But in practice, they can't. If they refuse a job offer, they may be unable to put food on the table, lose the roof over their head, etc. A bureaucrat may be breathing down their neck, threatening to cut benefits if they don't take a job. So in practice, they often don't have much of a choice.
When worries about job security (and income security that comes with it) are gone, that could have huge positive effects on the mental well-being of the population. Less fighting between spouses over money, fewer troubles between low-income tenants and their landlords, drug addicts that don't have to go out stealing to pay for their habit, etc, etc, etc. And that's not even taking into account that people will have greater job satisfaction when given the freedom to pursue the jobs they want.
I think over time, the way things are currently done, simply won't work anymore and something will have to change if large-scale social unrest is to be avoided. A basic income would be a big step in the right direction, with potentially huge positive effects on society. The time is ripe for it, let's hope experiments like this will show it's a good idea and actually works.