Your leads/customers are not able to close the channels on your side, only you can close the channels by typing command “!close” or waiting for the automatic close.
What your leads/customers can close is the chat box on their side, but as long as they open it again, they can see the conversation history and go back to the conversation.
The conversation history will be always saved on the lead/customer side; he can either keep it, or clear the cookies to erase it. However, the conversation history will be always saved to your Slack and your Slaask account.
If you closed a visitor channel accidentally, you can get it back by following this article: Making Slaask work with archived channels.