For example if the cost of living is $1000 and you give people who need it $1000 then before long the cost of living would rise to $2000.

You may choose to have a $2000 cost of living, but you would choose that too through a pay raise. You could be empowered to keep $1000 cost of living, and there would be more apartments like "yours" if everyone else is moving up in lifestyle.

UBI gives you more choices. If you think everyone else is passive, just paying what they are told, you can use the opportunity to build more affordable life options for people, including easy access to loans from all of the extra money getting spent.