Dovecot can support mailbox sharing in several different ways:
Public mailboxes: Shared mailboxes created by administrators (ACLs can still restrict who sees them)
Shared mailboxes: Users sharing their mailboxes to other users (using IMAP ACL commands) (v1.2+)
Symlinking mailboxes: Quick and dirty way of sharing a few mailboxes.
See SharedMailboxes/Permissions for common filesystem related permission problems that are common with all the sharing methods.