Closing chats move them from the inbox to the closed folder. Closed chats still exist in your account and can be searched. It's similar to closing emails or documents. You can always open chats and move them back to your inbox.
When a new message is received, the chat will automatically be moved back to the Inbox and be marked as unread.
Marking Chats as Read
Your unread count is user specific. Each teammate has their own unread count based on the chats they have not yet viewed, so marking a chat as read only affects your view, not your teammates'.
Opening a chat automatically marks it as read and removes it from your unread count.
To clear all unread chats at once, set the filter to Unread (from a specific inbox), then select Mark All as Read at the top of the chat list.
Confirm when prompted.
All chats in the current view will be marked as read.
If a new message arrives on a chat you have marked as read, it will return to the Inbox as unread.