This is the problem with basic income if you don’t also increase the housing supply: landlords will just raise rents and soak it all up.
Or you could have progressive real estate tax so you don't let the bully keep the stolen lunch money and you can give it to your kid again.
It does, however, make providing housing more profitable, which, on the margins, will drive more landlords and home builders into the market, decreasing long term costs (relative to a straight 100% increase relative to the basic income). So you might send everyone $100 per month and costs go up $100 per month, until supply chains shift towards supplying lower income humans with more goods and services than they used to get, at which point costs will decrease (from the $100 increase).
With enough forewarning, suppliers could anticipate the increased demand and prepare for it.