Initially there is some magnetic flux associated with the solenoid, but when current in the circuit stops, the magnetic flux falls to zero or magnetic flux associated through the ring decreases.
According to lens’s law this decrease in flux will be opposed.
As the current decreases, it will cause a clockwise current (as seen from the top of the ring) to increase the decreasing flux. Which can be done if the direction of magnetic field is same as that of the solenoid.
So, the ring and the solenoid will attract each-other but as the ring is placed at the cardboard, it is not able to move downwards. But the upward reaction of the cardboard on the ring will increase.
Final answer: The upward reaction of the cardboard on the ring will increase.