can i unpublish a site?

UNDER CONSTRUCTION?
You can unpublish from the file manager. Click on your site name on the top right of the editor. Open your File Manager, select your pages and files, and un-publish.

You can create a text box: "Under Construction" or whatever you want to use to identify your site's condition. Expand the text box to cover your menus, add a color background to hide the contents, use text centering, borders and padding to create a nice presentation. The same thing can be accomplished using any image. Be creative. Covering the menus will prevent access to other pages without having to change the status of your site. After, save and publish. Using this alternate method, you can work on your site by lifting the cover and insert images, text etc. You can Save your work without changing the published presentation. When you're ready, remove the facade save and publish.

Are you using SiteBuilder Plus? I should have specified.

Thanks for the alternate instructions. That will work in almost any situation.

But the title of my site is not listed at the top of the page. maybe it is called Website Builder. It's the latest version.

Ok. I just made a replaced the home page with a new one that says Website Not Available and I hid all the other pages from the menu so it is not accessible. Thanks for your help :)