Restrict customer to reply on closed widget message window

We are planning to onboard our chat support service on Zendesk but we hit a roadblock where we got to know that any old closed chat conversation can be replied to by the customer, which will internally create a new ticket, but the customer will think that they are referring to the existing chat. This will build an understanding gap between the agent and the customer, leading to multiple bad customer experiences.  Ask is to provide a configuration that can disable the reply text box when a ticket is marked closed so that customers will create new ticket for any new issue instead of working on the same window.

Whenever chat is closed, then if customer close chat window and reopen it then they should be shown navigation window of all the chat instead of closed chat as that create confusion for customer