Use add_filter on concatenated string variable

As @Sally mention in the comment.
if you want to let others to extend the HTML code.
you should also append the new HTML they returning in the filter.

Try code below

$admin_table_output .= "Item Description: </td><td>";

$admin_table_output = apply_filters('tabs_page_static_value',$admin_table_output);

$admin_table_output .= "<input type="text" name="name" value="$name"></td><td> (Optional)</td></tr><tr><td colspan='4'>";