Why are there folders in /Users of already deleted users?
TLDR: Deleting this user's home folder will not harm your system. It will, obviously enough, delete any of the files you created when you were logged in as the previous user.



How is it possible that there be a folder for a user who doesn't appear at the login window?

OS X keeps track of users and their passwords using Directory Services. On most people's computers the Directory Services files are stored in /var/db/dslocal. This database stores the names of users, and other information, such as the location of their home folder. When you deleted your user, your Mac removed the account entry (from the dslocal database), but did not delete the home folder stored in the /Users folder.



So why didn't the system automatically delete the home folder when it deleted the user from the database?

When you delete a User from System Preferences, you are asked what to do with the home folder itself. You can see from this screenshot which option you must have accidentally chosen:





What's the best way to delete the old user's home folder?

I would suggest logging into the account one last time to ensure it does not contain any files you wish to keep, and then deleting both the user record and its files (as you originally intended). To do so:


in System Preferences > Users &amp; Groups, create a new account with the exact same name as the old user's home folder. The system will ask if you wish to use the existing home folder. Choose to do so.
From the Apple menu, choose "Log out" and then log back in to the old user (ie: the user you just recreated).
Take look around in the user's Pictures folder, Documents folder, etc to make sure there are no files you wish to keep
Log back in to your normal account
Delete the old user from "Users &amp; Groups" but this time, choose "Delete the home folder"