TDI high-pressure fuel pump (CP4) failure
Diesel models use a Bosch CP4 pump that can grind itself apart without warning, sending metal through the whole fuel system. The car stalls and will not restart, and the fix often means replacing every fuel component. There is no test-drive tell — ask for records of any pump work and factor the risk into the price on any TDI.
Ask for repair records covering this item. If it hasn't been addressed and the car is in or near the mileage window, price the $2,000–$7,000 repair into your offer — or make it the seller's problem.