Rolla was the jumping off place for the Union army for the southern part of the state. It became the major Union base of operation. Confederate sympathizers were brought there for court-martial. Fort Wyman in the south part of town was constructed to prevent a southern attack of the town but instead became a holding pen for prisoners. Men and women were kept there until their trials or bonds could be posted. The Old Jail, next to the Old Courthouse (both are still standing and are preserved), was full of prisoners as well. A short distance from Fort Wyman, on the same ridge, is the Old Rolla Cemetery which contains the soldier's graveyard. Union soldiers who died, for various reasons, were buried there.
With all this being said, I am familiar with the local burial sites of many who served in the Confederacy (including my GGG-grandfather Green Berry Harris) but I need more info about this marker you described. Can you give me its location? I know of one place on HWY 72 which has a stone as you describe.
Rolla was not attacked by the rebel army but bushwhackers and Confederates heading south passed through the area constantly. Skirmishes took place between Union cavalry/militia and rebels throughout the war and after.