I'm trying to filter ALL widget output through a simple filter, but can't find any hooks and was hoping to be pointed in the right direction. Or possibly my efforts are not even possible?

My simple filter is something like this:

function clean_widget_output( $input ) {
    return str_replace( array( "\t", "\n", "\r" ), '', $input );
}

add_[FILTER OR ACTION]( 'need_a_hook', 'clean_widget_output', 99 );

Any ideas? I'm pretty new to PHP, but I can get around.