The solution I can think of is removing the panels Available and Inactive Widgets so there’s simply nowhere to drag (and delete) the widgets used in the sidebar.
You can inject something else to fill the gap.
In this example, only one user is able to add/delete widgets.
function wpse_53398_script_printer(){
// used to display the front end site
$site = get_site_url();
// here you can filter who can add/delete widgets
global $current_user;
if ( 'kursus' == $current_user->data->user_login )
{
echo <<<HTML
<!-- CSS to hide the widgets descriptions = real estate gains -->
<style type="text/css">#widget-list .widget-description {display:none;}</style>
<script type="text/javascript">
jQuery(document).ready( function($) {
// swaps the placement of the panels Available Widgets and Incactive Widgets
$('#available-widgets').appendTo('#widgets-left');
});
</script>
HTML;
}
else
{
echo <<<HTML
<!-- CSS to prevent the div from briefly appearing before the jQuery can act -->
<style type="text/css">#widgets-left {display:none;}</style>
<script type="text/javascript">
// reload the contents of the iframe
function Reload () {
var f = document.getElementById('the-front-end');
f.src = f.src;
}
jQuery(document).ready( function($) {
// inject other content to fill the void
$('<div style="width:70%;"><input type="button" value="Reload front page" onclick="Reload();" style="float:right"><br /><iframe id="the-front-end" src="https://wordpress.stackexchange.com/questions/53398/{$site}" frameborder="0" width="100%" height="700"></div>').insertBefore('#widgets-left');
// removes the whole left side of the widgets page
$('#widgets-left').remove();
});
</script>
HTML;
}
}
add_action('admin_footer-widgets.php', 'wpse_53398_script_printer');
Important: the HTML; closing line cannot have any whitespace characters before or after
PS: this Heredoc syntax <<<HTML code HTML; is preventing the code to display the PHP properly formatted here in WPSE. But the code is tested and working.