What happens when the ground reference is disconnected from an electric circuit?

Current stops circulating only if the ground is part of the circuit,  If it's just the third (ground) prong of the outlet, you've only defeated a safety device; the current will still circulate from hot to neutral.

In most circuits having a real ground is irrelevant.  The circuit works because there is a potential difference and electrons are driven through the circuit.  A ground is only something that provides a zero reference voltage and this does not matter to most circuits.

One area where a real ground is needed is when things interact with the circuit or might interact with the circuit and you want to be sure that there is not a significant potential difference between the circuit components and the objects near the circuit.

Whether the ground reference is connected or disconnected is not a matter, as long as the circuit is a closed one.

If and only if the circuit is not closed or is open as the ground is disconnected, the current will cease to flow. If not, there will be current.

The current through a circuit depends on the potential difference between two points and as hence the actual potentials of the points under consideration can be changed at our will.

Consider two points which are at + 10 V and another at ? 2V and there is no ground reference.
The potential difference between them is 10 ? [? 2] = 12 V.

If the negative point is earth connected, then the potential at that point becomes zero and the positive potential becomes 12 V with respect to ground.

Again the potential difference is 12 V.

But the circuit is a closed one even if we remove the earth connection. On removing the earth connection, the p.d remains the same as 12V and there is a current.

Instead, if we have cut the circuit at the negative potential point and the two terminals were connected to earth by two separate wires, on disconnecting one of the wires the circuit becomes open and the current stops.