When deleting user account(s) from IMAP server don't forget to put full server name and port. Also need to be logged as IMAP admin and set ACL.
This worked for Cyrus:
<?php
//Credentials
$cyrusadmin_username="cyrus";
$cyrusadmin_password="cyruspassword";
$cyrus_serverip="fellowship.ring.net";
//User to delete
$username="frodoBaggins";
//Open the connection to IMAP server (Cyrus)
$mbox=imap_open("{".$serverip.":143}",$cyrusadmin_username, $cyrusadmin_password, OP_HALFOPEN)
or die('IMAP Could not connect because '.imap_last_error());
//Set ACL - Give rights to $cyrusadmin_username to delete mailbox
imap_setacl ($mbox, "user.".$username, $cyrusadmin_username, "lrswipcda")
or die('Could not setacl on mailbox');
//Delete mailbox
imap_deletemailbox($mbox,"{".$serverip.":143}user.".$username)
or die('Could not delete mailbox');
?>