What happens where -- what does the circuit actually represent?
If this schematic is a lumped element model, it is either incomplete, or contains singularities:
For an ideal switch, turning off into a charged ideal inductor, the inductor will discharge instantaneously -- generating infinite voltage for zero time, with a total area under that curve corresponding to the flux it was charged to. A Dirac delta. The voltmeter still reads zero.
If we complete the circuit so it is well-defined and finite, then there is some shunt impedance on the switching node which defines the voltage, and the switch may have finite turn-off speed (in which case, its V-I characteristics during turn-off also matter).
If this schematic instead represents a physical arrangement of components, then it matters very much what those components are, and how they are arranged. (Indeed, a real switch will most likely arc in this case.) The voltmeter may or may not read anything, for a number of reasons -- most of which are not described by the diagram as shown, and so are not obvious to the casual observer.
Usually, we like schematics to be somewhere between these two cases: enough components/elements to capture the desired behavior space, while omitting information that isn't relevant to it.
Tim