She technically was not fired.

She had a contract, with options. Just like artists have with recording contracts. normally a 1 album deal with X amount of options. If your album tanks they company does not have to pick up the additional/possible options. So she likely had a 1 year deal with X Factor with options if she did well or the show overall did well. Obv. it tanked! And her option wasn't picked up!

So she wasn't fired, but essentially she was. Same thing happened, she lost her position. So whichever way you look at it. She lost her position. We normally do call that being fired.