Assuming the UBI works out as intended and doesn't lead to unmanageable inflation the definition of destitution will just change to reflect the new floor.

How many 70s government housing project apartments or leaky rural shacks do you think you'd need to combine to get one working set of appliances and utilities that every section 8 apartment and double wide trailer has these days? (I'd put that number at 3-5). That was the floor then. That floor is mostly the subfloor now.

As things get better our standards get higher. Progress is good but you will never "solve" poverty, destitution, or any other bad thing that is defined relative to the rest of the population.