When the cereal rye is dead much more sunlight will teach the soil and stimulate the growth of weeds unless another crop is planted and out competes them. Seeds from the dead cereal rye will fall to the soil and then germinate which will be the wrong time of year for cereal rye (not when the day length is correct to plant cereal rye) and the crop won’t perform well.
In addition, each rye seed that was planted and germinated likely has produced 50 to 100 times as many seeds. This will result in a stand that’s way too thick to be productive.
If the goal is to improve the soil, then polycultures or multiple species produce much better and faster results than monocultures. You might check out the blends at GreenCoverFoodPlots.com for more information. There are some webinars on that site by Dr. Jones that are very informative.