When you find your files are lost on an external hard drive, you can recover files from it on Mac with data recovery software such as iBoysoft Data Recovery for Mac as long as the data haven't been overwritten.
As you said that the folder is empty but the drive space hasn't changed. It is possible that the lost files are hidden so that you can not view them on your external hard drive on Mac. Thus, try to unhide files on Mac with the shortcut command-Shift-Period(.) or the following command lines in Terminal.
defaults write com.apple.Finder AppleShowAllFiles true
killall Finder
If unhiding files on Mac doesn't make the lost files on the external hard drive show up, you could check the Mac Trash where the deleted files go to. Perhaps, you accidentally deleted those files and they are moved to the Trash, still occupying the disk space of the external hard drive. If so, put the deleted files back from the Mac Trash.
Unluckily, both of the above methods don't work to restore the lost files on the external drive, then perhaps there is corruption on the drive making the files invisible. Then, you could try professional data recovery software which could recover files from an external hard drive external that is damaged, corrupted, formatted, unreadable, not showing, etc., iBoysoft Data Recovery for Mac stands out for its high recovery rate, risk-free environment, and easy-to-use interface.
Just download, install, and launch this software on your Mac, then freely search for lost/deleted files on the external hard drive, freely preview the scanned result, and recover the desired files to a different location.