That's an interesting idea, but I expect the result to be of low quality.
I suppose you are thinking about a computer program that compares one static frame of the background with other frames where somebody moves in the foreground. All pixels that are the same in both frames (within some narrow tolerance) will be made transparent for a new background. The static background frame has to be taken from the same video and the camera be fixed to avoid differences due to changes of perspective.
But the problem can best be seen with a difficult scene: Let's take a person with blonde hair in front of a pine wood book shelf. There will certainly be parts of the hair detected as background and vice versa. With a still photo this misdetection may be acceptable, but in a video with moving head and hair the separation between fore- and background will appear as a dancing artifact.
Other scenes may be easier. You just have to increase the contrast between fore- and background for example by using hair lights and exchange a dark original background with a dark new background. And of course film in the highest resolution and quality possible.