My thought is that this rarely, if ever, happened, and certainly was not an implied function of file closers. My reasoning is that a colonel giving open orders to those several ranks below him who are not officers commissioned by the state or federal government, but rather citizen soldiers like those they served with, goes against the entire idea of having citizen soldiers.
I also doubt many incidents of men actually killed outright by file closers in the 1860s, but don't doubt there were some given the scale of the war. But the platoon officers and NCO's had the authority to do it where warranted. And even if they did it, it was not something to talk about. The deceased was just classed as
killed in action.
The 1860s Volunteer Troops, once mustered into service they were in the Army, and subject to the Rules and Articles of War (of 1806) and the Regulations, etc. And Article of War no. 52 noted for misbehavior in battle, "shall suffer death,"... Or, by court-martial such other sentence as shall be ordered...
Ergo, one's life was forfeit, whether sentence was delivered by court-martial, or "instant" by a file closer, if at all. The Volunteer and Militia troops of the USA from 1861 were specifically by law placed under the authority of the Rules and Articles of War... just like the Regulars, etc.
Not any different in the Confederacy particularly.
In the 1700s, the authorities were clear about the subject of instant death at the hands of file-closers or platoon officers in action for misbehavior... From 1755, General Wolfe's instructions...
General Washington had called for "instant death" to those who misbehaved. At Trenton...
At Stony Point too...
General Zebulon Pike's orders for the assault upon York, Upper Canada, in 1813:
Most of the accounts from the 1860s that give the dirty details of discipline, mention the officers just whacking the men with their swords, or threatening with pistols, or the sergeants prodding some, here and there, with their bayonets.
George Evray with the 16th Michigan was familiar with the rules...
From Vicksburg...
Lt. Hydorn of the 72nd New York at Chancellorsville...
In 1861 Gen. J.E. Johnston of the Confederate Army ordered instant death to any man who quit the ranks in action without permission, particularly in claiming to assist the wounded...
Sergeant Drewry Easley of the 14th Virginia was a file closer, and bashed a shirker with his gun during Pickett's charge...
Col. Oates of the 15th Alabama...
"bosh" as in empty words, poppycock, etc.
Regarding Chickamauga, Oates recalled...
General Forrest shot down men who turned their face from the foe, and instructed his officers etc. to do likewise...
General Meade approved of instant death to deal with any misbehavior in battle, from June 30, 1863:
The veterans of the 155th Pennsylvania recalled on the reading of this Order from the Commanding General before marching that day, that some of the soldiers felt
concern for their comrades who had straggled in the previous days and not yet caught up....
The veterans of the 13th Massachusetts grumbled about the orders of the new Army commander:
Regardless the orders stood, and some subordinates made use of the authority given. General Gibbon on July 2 gave direct orders for instant death at Gettysburg to shirkers... The veterans of the 1st Minnesota noted:
In the wake of Meade's standing orders, etc., Elizabeth Blair Lee, daughter of Lincoln's advisor Francis P. Blair, and sister of Postmaster General Montgomery Blair, and General Frank Blair, who commanded a division under Grant at Vicksburg, wrote her naval officer husband that it was considered a great turnaround in affairs...
General E.M. Lewis of the US Army, in the late 19th Century, noted that the basic discipline of instilling mortal fear of the officers and NCOs, by no means the best, it was yet necessary to be able to threaten use of the authority behind it, even though by then almost universally employed in extended order in action (capable of taking cover)...