I have a video with multiple moving people, from which I would like to remove one person. I know this is possible and that software exists to do it (see this paper), but I can't find any available to the general public.
You could export the video to still frames, then the problem is reduced to removing the person from pictures.
You can use Gimp or any decent paint program with a clone tool to copy sections of a good image to the image that needs correcting. The clone tool is pretty quick to use. But yes, at 30 fps if your perpetrator is in the scene for 5s is a lot of frames to tinker with.
Adobe After Effects has the ability to fill based on previous frames which works fairly well if the camera is stationary. Basically it pulls pixels from previous frames where the person isn't there and places them over the person. It can extract the person because it is easy to tell what pixels are changing and look for a group of them from frame to frame.
There are some major limits though. If there is anything else moving in front or behind the person, then there isn't an effective way to distinguish the person from the other object. Similarly, if the camera is moving at all, then both the background to fill in behind and the reference of what is stationary go out the window.
In cases where it can't be automatically processed, it would be necessary to rotoscope the person out frame by frame. After Effects is also capable of supporting rotoscoping pretty easily as well, though it is a time consuming process.