This improves the supply-side of the economy, but doesn't do anything to stimulate demand for products. Today, lack of demand is a larger problem than increased output. The labor share of GDP has been decreasing since the 70s, and its starting to hit levels where people are having trouble affording as many goods. Although investing is a good use of funds, arguably redistribution (a type of demand-side stimulus) would be more helpful today.
So, then the poor will be left with decreased Social Security, Medicare, Medicaid, etc. But hey! At least they get 12K a year!
From your description, it actually sounds worse. As I read it, it sounds sort of like this.
1) Reduce Social Security (so steal people's retirement money that they paid in...)
2) Reduce Medicare / Medicaid (The group of people that receive these are often the one's least likely to be able to afford medical care (the poor & the eldery) while simultaneously being the one's most likely to need such care (at least the elderly)).
1) Cutting spending elsewhere.
2) Raising taxes. (Or collecting more from a growing economy.)
3) Printing money.
Probably it would be a combination of all 3, but since UBI can offset entitlement cuts it makes sense to me that that's where the government would find a lot of the money. Raising taxes is unpopular and can be counterproductive if done to the extreme, and printing money is inflationary and also counterproductive unless there are other deflationary forces at work. (Which there are currently, I agree with Ray Dalio that printing money makes sense during a deleveraging spiral https://www.youtube.com/watch?v=PHe0bXAIuk0)
I'm not an advocate of replacing all means-based programmes with UBI, but it should see a significant improvement over many such.
But I think the pro-UBI argument would be that you don't need to increase the money supply to do it. About 60% of Federal spending is on Social Security, Medicare and Medicaid. Reducing the spending on these programs, and other inefficient transfers such as welfare and disability will pay for much of UBI, and the rest is paid for by raising taxes. The net outcome is that rich people will pay a bit more to the government than they do now, poor people get a bit more than they do now, but the major effects are 1) inefficient bureaucracy is eliminated, 2) bad incentives are eliminated (such as disability payments forbidding any gainful employment, and 3) the stigma of welfare payments is removed when everyone gets them.
I don't think this will work in the US because 1) there's no political will to reduce existing entitlement programs and 2) there's a lot of resentment in the working class against recipients of entitlements, and 3) racism. However, the argument that UBI will fail because it requires printing money is probably wrong.