To test the electrics to the injectors on a Peugeot 406 HDi, you should first check the injector connectors for proper voltage using a multimeter while cranking the engine; you should see around 12V at the connector during cranking. Next, check for continuity in the wiring from the ECU to each injector. Additionally, verify the ECU's operation and ground connections, as a faulty ECU can prevent injector firing. Other likely causes for the engine not firing could include a lack of compression, fuel pressure issues, or a malfunctioning crankshaft position sensor, which can also be tested with appropriate diagnostic equipment.
check the fuses
Are you getting power to the system?
the computer and the ignition module give power to the injectors.
I never heard of any fuel injectors getting damaged from running out of gas.
blown fuse?
When all fuel injectors are stuck open, this generally means that the injectors are not getting the right voltage. You will need to not only check the voltage, but make sure the injectors are receiving the right signal.
Turn down the fuel getting to the injectors.
If it has a carburator it cannot have injectors. If it has injectors it cannot have a carburator. Take the throttle body apart and clean it very well with carburator cleaner.
They come out the top of the throttle body. Clean area thoroughly before replacing the injectors to avoid any dirt getting in to the system.
Get your local mechanic to bleed the injectors
Clean / replace fuel injectors.
Maybe fuel pump or dirty injectors