Maybe I am misinterpreting your drawing. My understanding is that the red force arrow acts on the green block to pull it down.
If you have two blocks with a frictionless contact between them and pull them apart, there will be no connection between them and no solution to a static structural analysis. The stress will be zero.
If you have two blocks and push them together, there is a connection and with sufficient other boundary conditions, there will be a solution to the structural analysis and the stress will be non-zero.
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