For whatever reason, you may leave an asylum at any time by going to its Asylum Info page and clicking on the "leave the asylum" hyperlink at the top. You will then also be given the option of removing the asylum from your friends list.
If the asylum you would like to leave has been deleted or suspended, and you can't view the Asylum Info page, you can go to the Admin Console [http://www.insanejournal.com/admin/console/] and execute the following command:
community [asylumname] remove [username]
When entering the command, remove the [ and ] symbols. These are simply used for reference purposes. Replace [asylum] with the username of the asylum and [username] with your own username.