So lower-income housing landlords do raise their rents. Grocery stores raise prices on their beef. Low-end used cars get more expensive. More dollars chase the same quantity of goods and services.
But basic income continues into the long run. It becomes a business opportunity to undercut those inflated prices, to capture more of the basic income flow for yourself. An entrepreneur builds lower-income housing and charges lower than the prevailing rents, immediately poaching business from the opportunist landlords, who now have to compete with one another to keep tenants.
As additional competitors enter the market, the economic allocations change to match the newer distribution of incomes. More businesses that serve lower-income people become viable, so more economic activity occurs to cater to that sector. Fewer businesses that serve higher-income people remain viable, because they are taxed more. It slowly becomes more expensive to be rich, and less expensive to be poor.
In the long run, wealth distribution flattens and is less self-reinforcing. More than a few people would be willing to walk a higher wire if they were given a stronger safety net, choosing risky entrepreneurship rather than safer employment. Prices only remain high if existing businesses are protected from competition.