Unknown Files Automatically Download

If the above doesn't work, is this happening when visiting all web sites or only certain web sites?

Try setting up another admin user account to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.

Isolating an issue by using another user account 

Safe Mode - About

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown.

Etrecheck – System Information

If the log won’t post, try posting it in Pastebin and provide a link in a reply        Pastebin

Nope. I have the same problem, it's not malware, it's not an extension, and it's not a bogus website.

Safari repeatedly downloads zero-length text files named "unknown" when loading arbitrary webpages. The webpages are completely benign, and have no downloads on them. Lots of people are reporting this. It's been happening to me for about a month now, but I can't recall whether it started before or after I upgraded to High Sierra.

You might want to consider starting a new discussion. Since this one is marked solved, less people are likely to look at it. A new post would be much more visible. You can link to this one.

All web sites or only some? Does it happen in another admin user account?

Then it sounds like the website your wife clicked on the was infected. If you deleted the files and it didn't return you're OK.

You're welcome.

Sounds like it may be malware. Download and run Malwarebytes. Malwarebytes was developed by one of our own colleagues here in ASC and is about the most proven anti-malware software for Mac.