This happens when the email address already belongs to an existing user or agent. Deskpro doesn't link the chat to that account, for security, so the new chat user is saved without an email address. This is expected.
How it works
When a user who isn't logged in starts a chat, Deskpro always creates a new user.
If the email entered already belongs to an existing user or agent, Deskpro doesn't link the chat to that account. Otherwise anyone could type someone else's email and get access to their tickets.
Two users can't share an email address, so the new chat user is left without one.
If the email address isn't already in Deskpro, it's saved on the new chat user as normal.