Is it possible for someone to sign on and not show their email address even to administrators of the site? She first signed on initially and it looks like she was on the next day. But there isn't an email address listed. I can see she has a password. She might be deleting the email address before she exits the site not sure. She doesn't want her information getting back to any family members still living in town.

You need an email address to register and login so she might be deleting it but still logged in via the login cookie if she is using the same computer. If she wants to login again she'll won't be able to without an email address. If she does not want to share her current email address she can go open a free email account at Google and use that email for the site.