Emulator

Open up the Emulated Wiimote config window, type a relative filepath into the Profile box, and hit Save. The window will save the profile, but can't find the created file so it looks like it just disappears.

Examples:
Type "a/b" and hit Save. Profile gets saved as "[userdir]\Config\Profiles\Wiimote\a\b.ini", creating the "a" directory, but the file is not displayed in the dropdown.
Type "../../Dolphin" and hit Save. Profile gets saved as "[userdir]\Config\Dolphin.ini", overwriting the main Dolphin config file.

I recommend just disallowing paths.

On this note, typing a name that has characters that are illegal in the filesystem doesn't save anything but doesn't display an error either.