The sprouting stage is as far as the grain can go without being planted in the ground. Beyond that point the fodder will die, because it is no longer getting any nutrients for growth, unless you were to add some kind of nutrient that is used by those involved in Hydroponics.
Fodder as it relates to what most people are referring to in this thread is really 7-9 day plants, that have green growth on them usually about 6 ish inches tall. With enough rinsing completely doable w/o adding nutrients and just a rudimentary "hydroponics" of pouring water over a tray w/ holes in the bottom several times a day.