Yes, both my Fluffikins and my Kiwi (lol) lost all tail feathers. Fluffy was in the cage with Mystery and Killer, last spring, and I think the three of them actually got into a nasty argument over Mystery. (She was in the process of bonding with Killer, and I'm the idiot that put 2 males and a female in the same cage.) Then when we got Kiwi, she was a duck butt within a day of being here.
It's kind of funny to see them without tail feathers, but as Goldielover said, they grow back quick and it's pretty normal.
Kiwi must be a very common name for a Budgie, lol.