Quick question, not so quick answer.
The short of it is, yes, if your boss wants to fly First on miles with UA and there are no Saver awards available, then she’ll need to pay the higher Everyday award fare.
The upside is, it’s possible UA may release more First Saver award availability closer to departure but it’s not a certainty. If your boss booked her flights on UA metal using UA miles, and Saver awards later become available, she can cancel her original booking and have the miles redeposited (and taxes/fees refunded) with no redeposit fee if she cancels more than 30 days prior to departure. The miles are redeposited immediately and become available to use to book the Saver awards. For awards canceled within 30 days, there is a $125 redeposit fee.
It used to be that UA would release Saver awards when they opened their schedule, some 330 days out. That’s no longer the case. There may be some Saver awards released at schedule open or a few weeks later, but UA could also wait to see how the flight is selling. So it’s not necessarily the case that First Saver awards were booked up a while ago. They may not have ever been released. If sales are lagging, UA may release some more award seats, especially as they get closer to departure. If sales are good and they think they can sell the seats, the chances of releasing more award inventory is lower. Unfortunately, there’s no telling if/when UA will release more award inventory. You can check frequently, or sign up for alerts through services like ExpertFlyer or SeatSpy.
Good luck!