They can also be non-text, filesystem orphans for which no application currently remains available to open them. Thus, they fail the magic file test, and the operating system tells the Finder to assign them the exec icon.
One file type that exhibits this orphan exec behavior is old AppleWorks .cwk files on Lion and later. Even on a machine that has Pages '09, or LibreOffice installed, either of which can open the .cwk word processing files, or other AppleWorks file types if LibreOffice alone.
The OP will not be able to open these files without the installation of the application that created them. Since the OP was recently opening these files, the question would be what application was removed, or is on an unmounted external drive?