The New York Times has reported that many states are running quite low on the amount reserves that their unemployment trust funds have. In fact, 15 states have fewer than 4 months of reserves remaining, and with unemployment rates rising, and more and more lay-offs being announced each week, there's going to be more states that will be running low on funds.
When a state does run into trouble, they can borrow money from the federal government. But eventually, the state will need to start collecting more unemployment insurance premiums than the money they are paying---so that means eventually raising the UI premiums that employers must pay (or else reducing the unemployment rate).
You can read the entire New York Times article here.