What happens to your car when it has old motor oil in it?

The age of the oil isn't all that important; you can drive with old oil. The problem is the tiny metal flakes that wear off of the engine parts, and soot and carbon particles left behind in the cylinder when the engine runs. Your oil filter is supposed to filter those out, but it isn't perfect.

It's actually more important to change the oil filter than it is to change the oil, but it's generally not practical to try to catch and reuse the oil, since removing the oil filter normally allows all of the oil to run out.

The soot and particulate matter in the oil causes excessive wear, which will eventually require expensive repairs.