In most of the US, I believe there are no laws. California recently passed some legislation limiting rental increases per year, but it's still something like 7-8%, which is ludicrous.

The first world country I'm from has, effectively, nation-wide rent control (varies by region) and rent increases are limited to something around 1%, set each year (tracking inflation somewhat).

In the US, this will work very poorly: a landlord can just bump your rent by exactly the UBI amount and get away with it. Otherwise, they would have to wait for a vacancy to set the rent. But eventually, I agree that the rent would just absorb the UBI in many cases.

In the country I live, rent is indexed and adjusted to inflation on an yearly basis. When the contract expires, parties have the chance to negotiate rent value at contract renewal to either increase it or decrease it.

Many big cities in the US have forms of rent control. Usually this is tied to a particular tenant, if the old tenant moves out the landlord can charge a market rate.