You can use a difference matte effect. Put your static background layer under the layer with movement and switch the moving layer to "difference" blending mode. It will only show the pixels that are different in the two layers.
This works, but only for limited applications. The problems come when a pixel that is part of the moving object is exactly the same as one on the still background. Then you will have a transparent pixel in your moving object. Also you need to have a very good quality camera because if there is any slight lighting change in the Background or any artifacts that pixelate, you will have holes in what is supposed to be your BG Matte. Either way you might end up doing a decent amount of rotoscoping.