Technically, I could do such a thing, so it is possible. (Not the word I used is could, not would...) It is, however, difficult. Especially if you are not on the same network as the target PC. As far as being on the network, I once watched a hacker exploit a hidden admin share (specifically, C$ - passwords are there for a reason, people) to force the target computer to share previously unshared folders and grant write permissions so he could download all the files in that directory. While downloading the files, they showed up to the user as "locked" because the target OS was a single-user version (WinXP Home in that case - Pro would have simply forced the file to only open in Read-only mode).

Now, this does not prove that the files were definitely being downloaded - antivirus software could lock files during a scheduled scan, for example. Typically you would only notice this with large files if you tried to open the file after the scan has already started, or if you tried to save an open file that is being scanned. You may be able to check the computer logs for unauthorized remote access, and you should probably reinstall your antivirus software and rescan the computer.

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The best way to learn anything, is to question everything.