When you decide to quit before being fired.
You're too lazy or don't feel like caring to quit properly (school applies as well). You kind of had it coming. But you don't care, since you didn't show up for work for a week without calling (work). Or you miss the deadline to drop all classes (in university).
You can't fire me—I quitfired.
When an employer offers an employee the opportunity to quit before their employment is terminated. This opportunity is offered to give the employee a chance to avoid embarrassment and to make it less difficult to secure new employment. A compound word created from the two verbs most commonly associated with voluntary and involuntary employment termination.
"Why did you quit your job?" "Well, the manager called me into his office and quitfired me."