Horde webmail interface shows each email in the folder (Inbox, Sent, Draft etc.) with 'Invalid Address' as a sender and 'No Subject' as a Topic. Moreover, each of those emails are shown to be 0B size and delivered (sent) in the same time.
Horde cannot not parse the data provided by MailEnable from '_index.xml' file that contains the information about the emails in the folder.
Open the physical mailbox folder:
%plesk_dir%\\Mail Servers\\Mail Enable\\Postoffices\\<domain_name>\\MAILROOT\\<username>\\Inbox
_index.xml' (it will be generated automatically again).