If your vehicle is showing steering wheel locks up completely while driving, here are the most likely causes and the parts you'll need to fix each one.
The belt driving the power steering pump snaps or slips off. This causes an immediate, drastic increase in steering effort that most drivers perceive as the wheel being completely locked.
If the engine unexpectedly dies while you are moving, the power steering pump stops spinning. This instantly removes steering assist, making the wheel incredibly heavy and difficult to turn.
On modern vehicles, the electric steering motor or its control module can fail, overheat, or lose power due to a voltage drop, instantly removing all steering assist.
A blown high-pressure hose or internal failure of the power steering pump will instantly drain the hydraulic pressure required to help you turn the wheel.
A worn ignition lock cylinder or heavy keychain can cause the key to slip out of the 'Run' position. This can physically engage the mechanical anti-theft steering wheel lock while the vehicle is in motion.
Internal gears, bearings, or valves inside the steering rack can shatter and physically jam the steering mechanism, preventing the wheels from turning at all.