The Feds have made it abundantly clear that they have no interest whatsoever in how paid time off of any kind is managed. While some states have begun implementing laws regarding the use of sick time, NJ is not one of them. However, some municipalities within NJ have established certain requirements - you can investigate whether there are any such requirements where you are.
If there aren't, then however the employer chooses to apply it is what goes.
Two things I am tired of typing: 1.) A wrongful termination does not mean that you were fired for something you didn't do; it means that you were fired for a reason prohibited by law. 2.) The above answer, whatever it is, assumes that no legally binding contract or CBA expressly says otherwise. If it does, the terms of the contract apply.