When a workflow sends an email to the email address of the Contact in a Case record, the email will show up in the Messages subtab in the Case record. However, when the Contact replies to this email, it will not reopen the Case record.
When an email is sent to workflow, it will create a unique email address that has a domain of '@firstname.lastname@example.org'. This is the reason why the case is not reopened. When an email is sent from a case record, it will have a domain of email@example.com. This unique email address links the email sent to the case record.