Ceteris paribus, prices go up, and living exclusively on the unconditional basic income becomes less attractive. With a UBI, there's no reason not to work if you are unsatisfied with what you get from the UBI, since you don't lose subsidy for working. So, there's a natural negative feedback control system.
> What happens when the last wealthy people you could tax into paying for it flee your country with their money?
If people making profits in the country that could be taxed leave, then profit making opportunities open up that others could, and someone will, take advantage of.