If you harvested half a crop or less, maybe a lot less, can you apply less fertilizer for next year's crop. Jim Camberato, Purdue University Extension soil fertility specialist, says it depends upon which nutrient you're talking about, and what your soil test levels are in the field.
Nitrogen will most likely not hold through spring, especially if winter and/or spring are warm and wet. The only way to hold nitrogen is to seed a cover crop, if you haven't already, and hope that the roots absorb some of the nitrogen for the plant's use before the N leaches too far down into the soil profile where the roots can no longer get it.
Phosphorus and Potassium are a different story, however. If your soils test levels are low, then you should still apply recommended rates for next season no matter what the crop did this year. You will likely still get a yield response if the weather is more favorable.
If your soils test medium or higher, you may be able to back off both phosphorus and potassium rates. If you harvested half a crop, then you can probably back off from recommended fertilizer rates for P and K by about half.
The one exception is if you harvested poor corn as silage. Taking off the stalk portion removes a good amount of potassium. If the silage yield was poor, you may get by with applying the regular recommended rate of potassium. If you harvested a decent silage crop in terms of tonnage, then you may actually want to apply more potash than you would just for a grain crop.
Soybean yields didn't tend to be cut as much in most places, but the same rules apply. If yields were cut in half, you could probably apply about half of recommended rates of P and K, assuming your soil test levels are medium or higher.