When they close the tab, the conversation continues
Chat that dies with the browser session is chat that loses the customer. This keeps the thread alive over email and stitches every reply back into the same conversation.
One thread, two transports
If the visitor is not connected when you reply, your message goes out as email. Their reply comes back to a per-conversation address, is matched to that conversation, has the quoted history stripped, and appears in the thread as if they had typed it in the widget.
Return to the site later and the entire history is still in the widget.
Inbound mail from an address that is not the visitor is dropped, not impersonated.
Only mail arriving on your own verified domain, or ours, is accepted.

Nobody is left waiting
Say you are closed, up front
Set hours per site in your own timezone. Outside them the widget goes straight to the away message rather than making someone wait two minutes for nothing.
A promise, not a silence
If nobody has answered after two minutes, the visitor is told their reply will arrive by email, with the address they gave. If an agent answers first, the notice never fires.
Mail that looks like you
Verify a domain and replies come from support@yourcompany.com, with visitors replying to an address they recognise. Until it is verified, nothing changes.
Questions about email fallback
What stops someone guessing a reply address and posting as the visitor? +
Do agents get an email for every message? +
Who does the email come from? +
Explore the rest of the product
Try it on your own site
Fourteen days free, and about two minutes to install.
Fourteen days free, no card.