In Louisiana, slaves were sometimes "drafted" from plantations to work temporarily on state works, such as fortifications and river defenses. In the event that one of these slaves died (or escaped) while working for the state, the plantation owner could file a claim against the state and would be reimbursed. Generally, the reimbursements I've looked at were for between $1,800 to $2,200. These records can still be found in the State Archives.
Of course, if your son was drafted and sent off to war for the state, he was considered a soldier and there was no reimbursement to be had. Apparently, the situation for slaves was the same as for sons. Slaves killed while serving as soldiers were not eligible for any kind of reimbursement.
General Richard Taylor said, in his memoirs, that "It was a curious feature of the war that the Southern people would cheerfully send thier sons to battle, but kept their slaves out of danger."