There are problems that need to be solved, but the one you have here you just invented. Government programs don't work like this. They aren't pegged to revenue.
The problem you described with oscillations and feedback loops is exactly one of the primary criticisms of attempts at forcing the government to balance the budget each year.
A sane government behavior would be to spend in year n the known tax revenue of year (n-1), and nothing more.
With unemployment benefit the goverment automatically injects cash into the area to forstall this outcome.
This is only a problem for a government constrained to short-term budget balance (U.S. states largely are for their operating budgets, but the federal government is not.)
In the very long term, nothing is guaranteed, but there is no basis to believe that the tax base will drop by 50% next year, and ample reason to believe the contrary.
Add to this the fact that basic income takes away, at least some of, the reason to work in the first place, which means that the very foundation of governments paying out basic incomes -- income from taxation -- is affected by paying out basic income. The result is an unstable system with feedback loops, where paying out a lot of basic income one year results in fewer taxes the next year, which means the government has less money to pay out in basic income that year, causing people to need to a job, which increases taxes the next year, after which the government can pay out more in basic income. Predicting this oscillation is essential to making basic income work, and I'm not confident it's possible at all, at least not when we need to be as sure about it as we do when we're talking about money that people need to buy food.