I'll explain this issue with a bit more detail so the situation can be understood.

The only item in the fuel injection circuit that can "turn on" fuel injectors is the LH fuel injection module - which does this by completing the circuit between the fuel injectors (which are provided battery voltage when the ignition is turned on) and ground.

The only action that a failed relay could do is fail open circuit such that the LH would get no power (and would not work at all) - or fail closed circuit - such that the LH would always be powered (and would do nothing until the RPM signal is provided). Neither of these failures could cause the fuel injectors to "chatter" when the engine isn't running.
The fuel injectors should NEVER open when the engine isn't running.

The fuel injection cycle starts only when the RPM sensor (an inductive sensor at the flywheel) provides RPM signals to the EZK spark controller.
The EZK spark controller processes the RPM signal and provides a square wave RPM signal to the LH. The LH processes this signal to switch the "ground" path "closed an open" for the fuel injection circuit.

The fuel pump is not energized by the fuel pump relay circuit (that is controlled by the LH) until the engine spins at over 50 RPM and is de-energized when the RPM falls below 50 RPM. This is a safety feature, if the car is in an accident and/or if a fuel line is cut, then the engine will stop running. When the engine stops running, the fuel pump is then stopped (fuel pump relay opens). For this reason the fuel pump relay should never be powered by the ignition circuit (as some do to bypass this safety feature when the LH fails to provide ground to the fuel pump relay - another failure mode of the LH module).

There is residual fuel pressure in the fuel injection system after shutting down the engine. Clearly, when the engine isn't running the fuel injectors opening and closing is not proper, the injectors are spraying fuel into the engine when they do this and are flooding the engine with fuel. If the LH is doing this when the engine isn't running, it is very unlikely that the LH will be metering the fuel properly when the engine is running. Therefore, you should never attempt to restart the engine if the fuel injectors are clattering when the engine isn't turning. I suggest that the spark plugs be removed so that the fuel evaporates before it runs down past the rings and dilutes the oil.

The Porsche 1987 - 1995 Porsche 928 LH module is the one type of LH that exhibits this clattering injector failure mode, other LH module types don't do this. It is a sure sign that your LH has failed when this happened. This failure can be traced to the hybrid circuit on the LH controller board. The only fix is to replace this hybrid circuit, which is a part that is not available as an "off the shelf" replacement component.

'93 GTS
'87 S4
'79 Euro Track Beast