If the circuit isn’t complete the cell can’t gain and lose electrons in equal measure, it’s either accepting them *or* donating them.
This causes a buildup of charge, the donor becomes positively charged and the acceptor becomes negatively charged.
Since electrons are negative, they will not flow from a positive towards a negative for very long.
You may get a very brief trickle of current while the system charges up like a capacitor, but this will quickly go to zero.
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