If 10 families are in price competition for 9 houses* the price will be $1 more than the poorest family can afford. Which will probably leave the second-poorest family struggling.
If (in your justified pity for the poorest and second-poorest) you give everyone a free $1000, the equilibrium price will simply rise by $1000 leaving the same families struggling and homeless.
This is the model armchair economists use to explain reports that Bay Area employees paid 4x the national median household income can struggle to find housing.
Of course, if you instead think of Detroit, where many properties are abandoned and some change hands for as little as $500, the model is far less applicable.
*Assuming a simple model of a closed system where all houses are identical, there are no houses outside the system, no possibility of building new houses, and families are as densely packed as possible.
Bat Area employees pay so much because of gentrification, inequality and concentration of wealth.
A UBI is simply a progressive tax to counteract the usual economic forces that let the richer get richer: they can afford bigger switching costs, they can afford to take more risks, they have amassed more patents and technology like AI, loyal engineers and so on.
UBI can be adjusted to simply redistribute the money in the system back so everyone has a floor, and can also afford to take risks without worrying about access to the expectations and necessities of modern life.
