That's an excellent and important question.

And the answer is that prices will probably be expected to go up to some degree as a one-time thing, in a way that would be approximately a wash for those already with plenty of income, but where it still makes a huge difference for those with little/no income, which is precisely the point.

For example if it's a one-time inflation bump of 10% and UBI of $10K/yr., then:

  Person A with income $100,000/yr, now makes $110,000/yr., worth $100,000 in previous dollars

  Person B with income $10,000/yr, now makes $20,000/yr., worth $18,182 in previous dollars

  Person C with income $0/yr, now makes $10,000/yr., worth $9,091 in previous dollars

Again, this is precisely the goal: the extra income isn't supposed to mean anything for those who already have plenty of income. It's supposed to help those who don't, or those who lose their jobs, etc. Without a big government bureaucracy trying to determine who qualifies or not.

And it's important to realize that the inflation is a one-time event. Prices will rise but then they'll stop rising. And if it were 10% inflation over a year, that's the same as the usual targeted 2% inflation rate but compressed from 5 years. (And the central bank might very well target 0% inflation over the following 4 years to compensate.)