Your rent would go up $250, which you’d be pissed about but you’d pay because you still have $750 from UBI.

Or, alternately, you'd look around the rental market to find a unit that hadn't arbitrarily gone up in price.

The scenario you describe only works in a very tightly constrained scenario where supply and demand are highly inelastic. In the real world people build new housing when demand rises, so prices don't spiral ever upward. Most of the places where there's currently a housing crisis hare having that problem because they've made bad zoning decisions due to NIMBYism and other such miscalculations.