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. And you can inject something else to fill the gap.
In my example, only one user is able to add/delete widgets.
Don't know why, but setting `display:none` was not working via CSS to hide the widgets descriptions, so was done in jQuery.
<!-- br -->
function wpse_53398_script_printer(){
// 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
$('#available-widgets').appendTo('#widgets-left');
});
</script>
HTML;
}
else
{
echo <<<HTML
<!-- CSS to prevent the div from briefly appearing befor the jQuery can act -->
<style type="text/css">#widgets-left {display:none;}</style>
<script type="text/javascript">
jQuery(document).ready( function($) {
// inject other content to fill the void
$('<div style="width:70%;"><img src="http://cdn.sstatic.net/wordpress/img/logo.png?v=123"></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 white-spaces before or after*
*PS: this [Heredoc sintax][1] `<<<HTML code HTML;` is preventing the code to display the PHP properly formated here in WPSE. But the code is tested and working.*
[1]: http://php.net/manual/en/language.types.string.php