Money isn't a "thing". It's not something tangible that gets printed or mined. Money is a representation of what humans value, relative to each other. Having lots of money is like having lots of momentum.
When monetary systems break down, for reasons such as a lack of liquidity, people fall back to the barter system. I'll give you a sack of potatoes for your hours of legal services. We're still playing the same game, but the "Monopoly Bank" ran out of paper, so we're using IOUs and direct asset exchange.
Being poor is just a state where the person lacks liquidity. Bank bailouts were enacted to "rehydrate" banks. Basic income is the bailout idea extended to the individual level.
Currencies are only valuable to you for 2 reasons: there's a finite amount, and other people value it (because they can also trade it for stuff). There's no finite amount of currency that satisfies a person; people can sense the total quantity of currency and want a fraction of this; this is why "printing money" or otherwise increasing the total pool of a currency causes inflation.
If Basic Income has a tax or other system to remove equal amounts currency from the pool, then the system might work; you would be transferring value from Producers to Consumers, much like many social programs do today.
But if there is no tax or other mechanism to remove currency from the pool, Basic Income will just create massive inflation, as the total amount of currency gets bigger, each piece of currency just becomes less valuable.
Basic Income isn't a different game. This is still the same economics. We're just adding another input to the system, everything still flows in, around, and out the same. Many poor people lack liquidity, but why they lack liquidity is because they lack something that other humans value more than their own money or assets.