I can imagine a situation when you are re-cleared from ILS to a non-prec approach that uses a different ground track, e.g. a VOR approach with VOR off the centerline. (sorry, can't remember how are those properly called).
Your airplane would not fly the VOR app track, but would try to intercept the ILS loc, even if you only planned to use that for reference. If the VOR approach is angled some 5° off the LOC, you can already run into quite a bit of distance error mid approach.