Here's a quick and dirty script to disable UnRegister. I created a custom User page. Added the User Account module. Then I added HTML text module below it. I believe it must be below it in order the javascript to work properly. After adding these two modules, I modified the text of the HTML module. I had to click the source button on the HTML editor and paste the code below into it then click update. If I use the HTML WYSIWYG editor of the HTML module, then it messes with the script.

I would appreciate suggestions if there is a better way to do this. Note: you will need to substitute "dnn_ctr518_ManageUsers_User_cmdDelete" with the id of the <span> element that contains the UnRegsiter code. This id can be found by logging in with a user other than an administrator, loading up this page (should show UnRegister button if javascript is not working), view the HTML source of your user page, and search for the <span> element which contains the UnRegister code.

<script type="text/javascript" language="javascript">
var theSpan = document.getElementById("dnn_ctr518_ManageUsers_User_cmdDelete");
if(theSpan != null)
{
dnn_ctr518_ManageUsers_User_cmdDelete.innerHTML = "";
dnn_ctr518_ManageUsers_User_cmdDelete.innerText = "";
document.write("UnRegister is disabled. Please contact the site administrator if need help with your account.");
}
</script>

Another issue with the Q&D solution is that the user can click on the username next to the 'Logout' link and is presented with the 'Unregister' link on that page as well.  This really needs to be configurable.  How do we go about making the request for the change?