Hook called before text widget save

Not sure what you’re after here, another options maybe possible, but there’s e.g. this hook:

/**
 * Filters a widget's settings before saving.
 *
 * Returning false will effectively short-circuit the widget's ability
 * to update settings.
 *
 * @since 2.8.0
 *
 * @param array     $instance     The current widget instance's settings.
 * @param array     $new_instance Array of new widget settings.
 * @param array     $old_instance Array of old widget settings.
 * @param WP_Widget $this         The current widget instance.
 */
 $instance = apply_filters( 
    'widget_update_callback', 
    $instance, 
    $new_instance, 
    $old_instance, 
    $this 
);

Here’s an example how we can target Text widgets and modify the text input field, when they are updated:

add_filter( 'widget_update_callback', function( $instance, $new, $old, $obj )
{
    if( 'text' === $obj->id_base && ! empty( $instance['text'] ) )
    {
        // Warning this overrides the widget instance text input:
        // $instance['text'] = 'override text';
    }

    return $instance;
}, 10, 4 );