Assuming we're talking about IMC conditions here.
Surely this relates to whether or not the aircraft is above the Minimum Vectoring Altitude or not. If the aircraft is still above the MVA then the clearance for the approach can be cancelled and an altitude/heading to fly can be given. ("Break off the approach" -never heard it used).
If the aircraft is below the MVA then I don't think the controller has the right to do anything except give you the standard missed approach until such time as you are above the MVA and can be given radar vectors.