The only time I've seen this done is in hybrid seed production. The farmer has to remove the tassel (the pollen-producing part) from all the seed row plants so that the silks receive only pollen from the pollen parent rows. In most cases that I've seen, the tassels are pulled, not cut, to cause as little injury to the plant as possible.
Where I come from, people refer to the cut stalks left in the field after harvesting the corn as the "corn stobs."
straw
I'm definitely not an expert, but from what I understand you can cut them down as soon as you harvest the corn. The stalk will not continue to produce as some other plants do. Once you harvest the existing ears of corn, the stalks are done. I just read a cute idea about saving the cut stalks and bundling them together for a fall / Halloween decoration :)
A sheaf is a bundle of cut stalks of grain or similar plants bound with straw or twine.
Combine harvester with a corn header.
Mexican work
There are many components that make up feed fro beef cattle, it really depends on where they are located, and the needs of the herd. Normally they are fed any feeds from the following list; corn, COB (corn, oats, barley mixture), insilage (corn cut from the field including stalks). Grains bought from feed stores may include molasses (for flavor) and added vitamins and minerals.
I'm not sure I am reading your question correctly but if your referring to the few rows left standing after the bulk of the field has been harvested it is to have a sampling of the field to show crop damage caused by deer etc. Answer #2, from Iowa Yes, vague question. Some corn is actually cut off a few inches above the ground to make what is called "silage" to feed cattle. The entire plant is used. Nothing is left except short stubble in the field. This is done earlier than picking, when the corn is still green. However, when corn is picked, only the ears are removed and the bent over stocks are left in the field. If a farmer uses part of a field for silage, it will be cut, leaving the other part to mature and be picked at a later date.
I picked corn a couple of days ago and one of my lower forearms is broke out in a rash. I sure hope it is corn rash. I am beginning to think it spread to my neck also. Itchy and blistered. Only showing up on my arm that was pulling the corn off the stalk. Very itchy.
a sickle was the main tool used by medieval farmers to cut down wheat and corn
i would cut them off
Cut down the corn. Clear as much plant debris as possible from the field. Leave some ears and corn in the field for the geese. I guarantee once one goose knows about it you will have hundreds of them there on a daily basis. I spent two weeks this past fall tracking the amount of geese and the times they flew into a neighboring cornfield for a snack. It was an amazing experience.