UBI will just cause inflation so that you have to work to afford things again. No company will forgo an opportunity to raise prices when they can. Fiduciary responsibility to corporate boards has always been more important than morals or ethics. And easier to get sued over. So boards will demand growth, as they do, and that will include raising prices where people can afford it. Poverty will still be there, it will just cost more (nominally) to get out of it.

The question you pose will remain with UBI, as will poverty. It might just get more extreme for anyone who gets disqualified from UBI for some reason (undocumented, etc).

This problem has not been solved for UBI nor seen in small-scale trials. But there isn't a single rich country or region in the world where the retail prices have not adjusted to consumers' spending power.

And people don't work at minimum wage if welfare is close enough to it. In my country it is rather popular to sit on welfare in countryside. Grow few berries to sell in local market for cash. Maybe help neighbour in a farm or construction for cash. At the end of the day you may stash more than minimum wage working few days a month.