So, this may sound like a silly question for some of you web masters but here goes...I have a client who wants to close their website but keep the email which contains the domain name it (ie. info@planbpropertywatch.com)...if they continue to renew the domain name can they keep their email and close the site?

yes this is possible.

Yes, you'd need to keep up the domain renewals, but otherwise this is perfectly possible.

I'd probably recommend using Gmail with your domain since it's free (Standard Edition) and reliable: https://www.google.com/a/

However, you'll also find various hosting providers offering "email only" services, or you could just take a hosting plan and not put a site on there - perhaps just create a holding page (or not) and setup your mailboxes etc. as usual.

Thank you so much for answering my question.