If user only has minimal permissions, current employer is blank when editing their contact record, and clicking save disables the relationship, even if the relationship setting allows the user to view/edit the org.

Create a (drupal) user.
Create an org contact.
Make the org the current employer for the individual contact you just created and set the relationship checkbox to allow the user to view/edit the org (i.e. the checkbox at civicrm/contact/view/rel&action=update&reset=1&cid=2&id=1&rtype=a_b)
Set up roles/permissions so that the user has just:
access CiviCRM, access CiviMail subscribe/unsubscribe pages, access Contact Dashboard, access all custom data, access uploaded files, make online contributions, all the profile permissions, register for events, view event info.
Log in as the user.
Go to edit their own contact record. The employer field will be blank.
Change something and click save. The relationship will become inactive.