I was actually a passenger in a car that was having an active oil leak. The driver knew what was happening, and was warned to pull to the side of the road and call a tow truck, but she wanted to try to make it home. Unfortunately, she didn’t. The engine seized up, never to run again. What a foolish and costly mistake.
The simple fact is that the engine in your car cannot run without lubrication from oil. Heat and friction would, as illustrated in the case above, cause the engine to come to a full halt.