No easy answer, I'm afraid. It will depend on many things, notably including the cause of the emergency and other traffic. Individual controllers' decisions will be affected by local policies and instructions. In some places, there is a view that a runway (or even airport) should be sterilised from the moment an emergency is declared until that aircraft is on the ground and all problems dealt with, in other places there seems to be no prevailing view. It's becoming common for the category of emergency declared at an airport (not the same thing as that declared by a pilot) to be determined by the problem reported by the distress aircraft, but I don't think I've seen any instructions that specify the point at which other operations should stop.