Fired?

So yesterday I got fired from my job (I think). My supervisor told me they decided to "let me go" because "things just aren't working out." Then she said that I was welcome to re-apply if I still wanted to work at the store, just not for the department I was in.

Here's what I'm wondering: if a person is fired from their job, are they not disallowed from working there ever again?

There should be a part on the application that says "have you ever worked here before? Why did you leave? Were you fired? If so why?"
Notice the "whys" they're important.