That depends on what program are you using to download. In mozilla for example, every time you start a download a file appears on the desired location (i.e. desktop)
Nameofthefile.exe
As you already know, It's a dummy file, 0 kb size, "incomplete" so it cannot be opened
Your REAL download is beign stored on other location, called nameofthefile.exe.part. Maybe it's located next to the other file, but hidden. Once the download is finished, Mozilla renames the .part file to nameofthefile.exe (to make it usable) and deletes the dummy file.
Your process is beign interrupted by something: The connection falls, the server is bad, they deny the file, whatever...
So the .part file is never completed, and the only thing you see is that dumb "nameofthefile.exe" 0 kb size file, every time the download is "supossedly" completed. And why not, this may also trigger the absurd administrator warnings.
Check your connection stability, or download the file from somewhere else and your problem will be gone