It can happen when one creates a new account to delete the existing one and forgets to make it an administrative account. Then logs in the new user, deletes the administrative user by supplying the admin password, et voilà, makes the Mac almost unusable.
All you can do is save the Apps you're interested to on a pendrive and reinstall from scratch. Licences of the paid Apps have gone one way or the other with the old user that was cancelled. You can use either the original disks, create a Usb pendrive, or reinstall via the internet if you have a fast enough connection.
https://support.apple.com/en-us/HT204904