It should be possible to search for it in Terminal (one can find Terminal via Spotlight, or in
sudo find / -name "AAProfilePicture*" 2>/dev/null
Various places come up with the profile picture, e.g. a couple here:
Once found, the search (
find) can be interrupted with ctrlC / or ^C
Directory Utility (to be found via Spotlight, or here:
/System/Library/CoreServices/Applications/Directory Utility.app) also shows the user's picture under the "Directory Editor" tab with the user selected and it can be copied from there. You may have to authenticate first.