What happens if tail feathers (or other feathers) fall out?
This means your budgie is probably molting. Luckily, the feathers will come back in no time, because the flight feathers in the tail are the most important for flight and essential for your budgie's survival.
Why do budgies lose their feathers? Feathers lose some of their insulative and protective qualities over time. If you wore the same clothes every day, the same would happen to you and eventually those clothes wouldn't keep you warm anymore. A budgie's answer to this is to generate a new bunch of feathers.