The gemara says that if the tzitz is broken, all agree that it doesn't offer kappara. The machlokes is only when the tzitz is in tact, but not being worn. Rav Yehuda holds that it is only מרצה while it is worn, and Rav Shimon holds that it is מרצה even when hanging in the closet. Why does the gemara speak about a "broken" tzitz, it could have said a simpler nafka mina such as when there is no tzitz at all?
Furthermore, the gemara says that according to Rav Shimon the reason that the tzitz is not mechaper when it is broken is because we darshen the pasuk - על מצחו ונשא, only when it is fit to be worn would it offer kappara. Why does the gemara need a pasuk to say that a broken tzitz is ineffective, it is obviously ineffective since it is broken?
It seems clear that the gemara specifically speaks about a broken tzitz, rather than there being no tzitz at all. The case of the broken tztiz is where the tzitz is still in tact, but it is broken in a way that it is unable to be worn without repair. Therefore, it still retains the status of a tzitz, so it would be possible that it is מרצה even in its present state, but Rav Shimon darshens from the pasuk that although the tzitz doesn't actually need to be worn, it only works to be me'chaper when it CAN be worn. The Maharatz Chiyus points out that the gemara is darshening the pasuk to require ראוי לבילה, meaning כל הראוי לבילה אין בילה מעכבת בו וכל שאינו ראוי לבילה בילה מעכבת בו. If it is fit to be worn, it works without being worn, but if it is unfit to be worn, it doesn't offer kapparah. Being that the tzitz is actually in tact, just "broken" from being able to be worn, Rav Shimon requires a pasuk to teach that it isn't מרצה.