Redirect user using the ‘wp_login_failed’ action hook if the error is ’empty_username’ or ’empty_password’

WordPress handles login failed in two ways:

1. If it is a bad credential, and both username and password have a
   value, then this action can be captured by wp_login_failed
2. If both, or one, of the options are empty, then WordPress generates
   the error object as the first parameter in the authenticate filter;
   it does not open and wp_login_failed action captures this
   cause/event

For what we have done here, see comments in code:

add_filter( 'authenticate', function( $user, $username, $password ) {
    // forcefully capture login failed to forcefully open wp_login_failed action, 
    // so that this event can be captured
    if ( empty( $username ) || empty( $password ) ) {
        do_action( 'wp_login_failed', $user );
    }
    return $user;
}, 10, 3 );

// to handle even you can handle the error like
add_action( 'wp_login_failed', function( $username ) {
    if ( is_wp_error( $username ) ) {
        // perform operation on error object for empty error
    }
} );