Generally, when someone replies to a forward, the reply will come in as a private note. This will not reopen the ticket. In order for it to reopen the ticket, go to Admin > Workflows > Automations > Ticket updates > Automatically reopen tickets when the customer responds and add a new event under 'Involves any of these events' as Note is added > any.

Once this event is added, the ticket status will change to Open whenever there are replies to a forward.