Engine Misfire: Troubleshooting & Repair

Hello fellow DIY enthusiasts,
After driving my father's Passat yesterday, I was very surprised by the strong jolting of the engine when starting and stopping it.
He hasn't cared about it until now, but this isn't a good situation. The engine runs perfectly normally, but it has this strong jerking when starting and stopping.
My question to you all is, what could it be? My friend thinks it might be a problem with the front pulley.
Vehicle data:
Passat TDI 1.9, 90 hp, engine code: AHH, manufactured in July 2000.