The bug manifests itself as follows:

1. A group can only be removed by one of its admins. 2. In order to remove the group, an admin must first remove its members. 3. Removing a group's members is a process that involves manually traversing a list of members and clicking a button beside each person's name. 4. The list of members contains the admin's name. 5. It is possible for the last admin of a group to remove him/herself as the admin of the group (even accidentally). 6. The only way to become an admin of a group is to be invited by an existing admin. 7. Therefore, if the last admin of a group accidentally removes him/herself, it becomes impossible to close the group.

I have attempted to contact Facebook about this with no luck. It appears that this has been a problem for people since December: http://www.facebook.com/topic.php?uid=10381469571&topic=13332#topic_top