I am reading Gettysburg The Last Invasion by Guelzo and it is recounted that a captain advised a sergeant to make sure that men who were chronic "playouts" be taken into the fight or killed by the sergeant himself. I assume the term means, men who avoided fighting but can find no such definition. Assuming I am guessing right, I wonder further how common dealing with such playouts by killing them was.
In Civil War usage, a "play-out was as soldier who was worn out or demoralized, possibly even to the point of a breakdown. The term also applied to one who was "suspected of malingering".
In context, it would seem that "chronic play-outs" would be more likely to be in the latter group.
Although some 500 soldiers were executed (by both sides) during the American Civil War, which is more than in all other American wars combined, this was nevertheless a relatively rare punishment. The vast majority of executions were for desertion, and were carried out in the later stages of the war.
Of course, those executions would have been carried out under military law. The situation that you are describing sounds like an extra-judicial, summary execution. While these may well have happened, there are unlikely to be much in the way of records in most cases.