I played single sims in S3, so I stayed on top of their careers. I can't recall any of them getting fired.
S2, I was playing it the day before. I had her join the teacher career. There might have been a chance card pop up before the 3rd promotion, but I must have picked the right one, LOL. She became a substitute teacher and filled in one day, the kids were terrible. She had a chance card come up asking if she should report the teacher (who was the best?) or ? (can't remember). I figured she should report it. It said she went into the office to tell the principal and the actual teacher was in there with the principal (I think). Anyway, she reported it and it came back that the actual teacher was in good with the principal. Next thing I know, the box popped up "YOU ARE FIRED". My mouth dropped open :o
Her lifetime wish was to be in the law enforcement (I didn't think to check that the first time, because I didn't remember them having that, or where to find it). She climbed up in law enforcement pretty quick but every time a chance card comes up, I hit "ignore", LOL. S2 is definitely the most challenging of all the series, but well worth playing.
Oh, in S4, I have not had anyone get fired. I usually only play the Dr. Career, or paint and collect for a living.