UBI can work only if the money comes from somewhere, and that'd be tax, to start with. There'd have to be some other kind of savings, though, to make it feasible.
The economists in favour of UBI envision that some, or even most, people will, once they have the breathing space of a regular, secure income, will fix their own finances, will start their own small businesses, some people to send their children to school, some people to improve the quality of their shelter and food, and that an array of these things will lead, indirectly, to improved health. Healthier and happier people are more able to contribute to the betterment of their environments, in their own homes and relationships, and in the area in which they live. If you're drop dead exhausted you walk on by that litter, if you're fed and fit you might bend down to pick it up and throw it away, and also go by to bring an old person some food, and so on. Similarly, people who can afford a toothbrush are more likely to keep their teeth healthy.
People who feel better and live in a better way are likely to consume fewer resources such as social workers (saving), medical services (saving), they'll be less likely to cause destruction of property (saving) and less likely to do anything which ought to involve a flashing light and a siren (saving). The articles I've read about UBI count on these concentric circles of societal cost reduction.
Add to that the entire machinery of all the offices that process applications for the existing, other kinds of grants and benefits, for assessment, for reporting and controlling: the economists in favour of UBI see that such offices could be eliminated altogether (saving). As such assessment processes are highly stressful for the subjects, departing from that kind of system would bring about a further postive effect on health.
In other words, they say, the UBI would not need to be funded directly 1:1 by a special tax, but the tax spending (on all of the above, other services) would be less, so some of that money could be redirected to the UBI.