Select some pixels from imported movie to duplicate and stretch
It is possible, but it might look a bit weird.  Video is constantly changing - even just a video of a wall will have noise in it, so static images tend to look a bit odd in comparison.  But Ii you stretch one pixel of the noisy moving image, you'll get lines of noise moving either side of your image, which might not look great either.

However, if you want to give it a go, duplicate your original image, use a mask to only show the edge that you want to extend, then adjust the scale in one dimension only (you'll need to click on the little link icon to only adjust the x-axis scale).

Alternatively, What many people do for a backdrop is to copy the image, scale it up to fill the screen, then blur, and darken it, and place it behind the original image.