Some important things to understand about Access security:
1) Access stores user profiles in an mdw file, not in the database itself. With a default setup, changing user profile information while in one database changes it for all databases you open while using that computer.
2) Any time you use Access, your permissions, etc. are determined by the mdw file to which you are presently linked.
3) The username displayed by Access at the login screen is the username that last successfully logged in to Access (even if it was a different database) using the current mdw file. This can easily be changed.
4) If Access does not let you login with a user profile, you have an error with the profile name and/or the password. The message displayed is the same if the username does not exist or if the password is incorrect.
5) There is always always always an "admin" user and a "users" usergroup. You can't get rid of these.
6) Access does not require you to login, or even give you the opportunity to login, if the "admin" user has no password. If the "admin" account has no password, Access automatically logs you in as this user without ever displaying the prompt. If you see the prompt, this account has a password.
7) In the default setup, the "admin" account has no password. If you are seeing the login, you or somebody else explicitly added a password to this profile.
8) If you are logged in as a user which doesn't have permission to change user profiles (and I suspect that Packaging is one such user), you will be unable to add/edit/delete user profiles.
Based on what you have described, I have reached the following conclusions:
A) You (or somebody else) added a password to the "admin" profile.
B) When the "packaging" user was created, it was not given permission to edit user profiles.
C) Thus, you must login as "admin" in order to remove the "packaging" profile.
D) To do this, you need the "admin" password.
D1) If you put the password on the "admin" profile, try every password you are likely to have used.
D2) If somebody else did it, speak with them to get the password.
D3) If somebody else did it, but they are unavailable, let me know so we can discuss what to do from here.