I am not an expert but had the hard shutdown and repaired it with a new fuel shut-off valve. The shut-off valve pulls the Injection Pump Rack out off "Run" position so that the fuel is denied to the system. If the shut-off valve is in the process of failing, the rack gets moved partially out of position and some fuel is allowed to pass. The result is a a degeneration from Idle to Rough Idle to Very Rough Idle to eventual Shutdown as the IP Rack is slowly drawn into the Shut-Off position. Before long the Fuel Shut-Off Valve will probably fail completely and the engine will continue to run unimpeded with the key in the "Off" position.

BTW, there is no exchange of air from the vacuum system to the Injection Pump. The vacuum pressure is used to draw the mechanism which pulls the Rack out of position.