Literally 100% of them will raise the rent and there won’t be anything anyone can do about it.
In addition, every seller of a good/service could do the same. They can't all increase prices to extract the full $xxxx a month. There are much more complex dynamics at play then just "landlords will raise rent enough to extract the full UBI benefit."
In theory, having more capital available in the face of a landlord raising rent an obnoxious amount will incentivize people who aren't making much to move somewhere with a lower CoL that they might not have been able to make work otherwise because of uncertainty in the amount of time they'd be out of work or their base level of money available for that time.