A current was flowing through the solenoid so it behave like a magnet and let $\mathrm{S}$ pole is upper side as flux in ring is constant, so no induced current in ring.
When the current is switched off, magnetic flux decrease through the ring. According to Lenz's law, this decrease in flux will be opposed and the ring experience downward force towards the solenoid.
This is due to the flux i decrease will cause a clockwise current, the same direction to that in the solenoid. That makes the opposite sense of flow of current in the ring 'when viewed from the bottom of the ring' and solenoid forming opposite magnetic pole infront of each other.
So that, they will attract each other but as ring is placed at the cardboard it could not be able to move downward.