I've used par files before. But they are usually .par and tend to be with .rar compression files. So if there are multiple .rar files it can make some .par files to repair the .rar file.
Have you checked the health of the hard drive?
I remember many years ago, back in the Win98, WinME days I had to keep reinstalling the OS as the hard drive would become corrupted. It would put weirdly named files on the hard drive that couldn't be opened. I wonder if this might be what is happening here?
Alternatively they could be left over files from a game or program that was installing, uninstalling or updating.
I wonder if a disk scan would work, or the chkdisk command etc. As long as the files aren't taking over then it's probably nothing to worry about in the near future.
Edit: Have you ever used a program called PowerArchiver ?