Earlier quoted context omitted.
What if it's not spare? It's their only $2000/month so they're not going to pay that much for rent, and someone else will offer lower prices to get that money. These same people aren't tied to a job, so they can more easily move somewhere cheaper too.
What landlord would continue to rent an apartment out for $X when it's easily possible to rent it out for $X+2000 or $X+1500 (not capturing the whole surplus, but a majority of it, say)?
Just because somebody has an extra 2000 dollars in their pocket every month doesn't mean they can earmark all of that money for rent; they surely have other bills that they need to pay as well. If the apartment was rentable at $X+2000, then why wasn't the landlord renting it at that price before everybody got the extra cash from UBI? Why do you think that somebody would say "Yes, now that I'm getting an extra two thousand dollars a month, my apartment is definitely worth an extra two thousand dollars a month" instead of saying "welp, rent is too high here, guess I'll move to some place else that's charging closer to what I used to pay"?