Tickets automatically reopen when there's a customer response because of an automation rule - Automatically Reopen tickets after the customer responds (under Admin > Workflows > Automations > Ticket updates tab > New Rule). You can modify this rule for it to not work for tickets that are 'Closed'.

Furthermore, when there's a reply from the requester on a ticket with status set to Closed, you can Trigger a webhook to create a new ticket with the latest response as the ticket's description (using placeholders). 

Here's the API documentation that will help you with the webhook.

If tickets have to be reopened when a customer responds, you can set up a simple rule by following the steps mentioned in this video.