Question about GPU memory shortage

When a CPU runs short on system RAM while processing we know it uses disk space as virtual memory. This slows down the computing process because the disk is a relatively slow device compared to system RAM.

How does a discrete GPU do this? If we say that video card "A" with limited GDDR amounts will perform more poorly on some games with high detail than the same card with twice the amount of GDDR ("B"), how does that work? Card A is still processing the job request. It really hasn't run out of memory per se. Why does the FPS drop off then? Is card A then resorting to system RAM or disk space as the CPU would to continue the game play?

To the best of my knowledge:

When a GPU runs out of memory, it has to wait to draw the next frame. This additional wait causes a stutter which is seen as lower frame rates. Card 'B' with twice the RAM does not stutter because it has enough RAM to render the frame and start to store data for the next frame. When you turn up the settings in a game, there is more data that has to be saved in RAM thus fewer frames can be held in reserve.

The trick is not only to have enough RAM to hold as many frames as possible, but for the GPU itself to have the power to process those frames to actually draw them out. I got caught by that with the Nvidia 5200. I bought a card with twice the RAM but the GPU could not process the data so I spent extra and gained nothing.

Not certain, but, I thought when it(game textures/data) fill up GDDRx, it spills over to system ram, which is why we see the hitching when it's transfering data between them (system ram is slower than GDDRx).