In the case of William G. Ellison, he actually was conscripted. About 30 men were conscripted at Camden in March 1863 and sent on to the 3rd Arkansas. They were the only known conscripts in that famous regiment, and had the bad luck to be conscripted at a time when an officer from the 3rd Arkansas home on furlough was supposed to take some volunteers back to Virginia with him.

Those poor conscripts had no idea what they were in for. Most of them were killed or died as prisoners of war, and only two were still with the colors at Appomattox. William G. Ellison managed to get back to the 24th Arkansas, however. He took French leave from a hospital at Richmond, somehow made it through the cordons of provost guards, traveled without authorization from Virginia to Georgia, and reported back to his old regiment in August 1863. Home at last!

I don't know on what grounds his conscription was authorized, but I suspect that he was just rounded up and sworn in, probably protesting the whole time that he was already in the service.