I think that cannons like most armament was supposed to be returned to the National armory. Later, I'm assuming, when their use is no longer needed, they (civil war cannons) end up in national parks and village squares. Complete original cannons are everywhere in national civil war battlefields.
Doubt that they are legally given over to private ownership. My town where I grew up had several CW mortars in the town square but they were put in storage when the town square was remodeled. Several years later, it dawned on some to ask what happened to them and the city had no idea and as far as I know, hasn't found them, yet. Obviously, they've been plundered by someone.
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Keep the chain tight!