Copper will kill a tomato plant, let me explain.
A copper nail into the base of a small tree will kill the tree. My neighbour had a Eucalypt (Gum Tree) growing near his driveway, but not on his property, so he drilled a 1/2"hole in the base and hammered in a piece of Copper Pipe. The tree eventually died - so I can't see placing copper near a cut tomato stem would reject the effects of the copper.
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