Most countries already have programs to prevent people from starving or freezing to death and those countries also tend to have elaborate health care programs, and provisions for those not able to work. Even the US has programs like this in most states though you could argue that compared to other countries they are a combination of expensive, inefficient, and ineffective.

Basic income is formalizing the status quo that there's a minimum standard for all that basically translates into everybody receiving those same guarantees but simply with less bureaucracy & moralistic BS around it. Basically it gets rid off or vastly simplifies the business of collecting and handing out social security insurances and different types of benefits. The cost for this in some countries actually rivals the benefits handed out. E.g. unemployment benefit programs have amazing amounts of bureaucracy associated in many countries.

For those who work, what changes is that part of their income now comes from basic income and they pay taxes over the rest. For their employers, they pay less salary and have less bureaucracy around things like insurance programs and social security (all taken care off). Also things like minimum incomes go away: they pay market prices for what somebody does for them. State pensions, unemployment benefits, sick leave compensation, etc. all basically fold into this basic income. If you want more, you work and pay for extra insurances yourself. If you don't, basic income is there for you.

For those that are not part of the labor market, i.e. approaching (or already over) 50% of the population in many countries, what changes is that their life becomes a lot simpler. Either they are happy enough to get by on basic income or they secure some additional source of income. Either way, we're already paying for their health care, housing, and food as as society. It's a much less radical change than people think.

IMHO this could actually unlock the labor market in lots of countries. There are a lot of weird rules around unemployment that actually make it unattractive or hard for people to work. E.g. people close to their retirement age are expensive to fire and therefore unattractive to hire in lots of countries. People on benefits are actually would risk losing their benefits if they take some job on the side. So, they don't work until they find something "proper", which for some never happens.

Of course this kind of debate always raises the question "who pays for this?". The people that ask this never look at the other side of the debate: how much do we save by eliminating and dismantling the byzantine bureaucracy responsible for the current system. Nobody has actually run that experiment.

Also, we have plenty of taxes left and plenty of wiggle room with things like VAT, fuel tax, profit tax and income tax. It boils down to a quite simple formula: total cost = X*#people. If you have say 17M+ people (NL, my home country) and assume 500 EURO per person, the total cost would be about 100 billion/year for absolutely everyone. Sounds like a lot but as part of the GDP (around 900 billion) it's not that bad and the that's completely ignoring the fact that this would make hiring people lower risk and lower cost for all companies; which tends to do wonders for their profitability (and thus profit taxes). The cumulative budget for existing programs in NL is actually similar to this.

Sadly, doing this is not feasible not for economical reasons but for political/moralistic reasons and ingrained (wrong/naieve) assumptions that many people have about how economies work (e.g. that they are balanced and circular). It's simply too radical for a majority. Even socialist/communist countries never went there and in fact had a lot of moralism and ideals around the notion of labor with the state actively trying to control who was allowed to do what and for how much.