Hello, I hope the following is of assistance.
The fuel cut off is electronically controlled through the engine management, there is a CAN link between the fuel injection pump and PCM if the engine is a TDDi. If the engine is a TDCi then the fuel is cut off by the engine management by shutting the IMV on the fuel pump and stopping the injectors from switching so not injecting any fuel.
If the fuel system has run out of diesel then the system will need bleeding before the engine will start again.
As this is all done electronically ideally you need to have a scan carried out of the PCM memory to check for any stored fault codes that would indicate a concern.
I hope this helps but if I can assist further let me know and I'll reply as soon as I'm able to.